Sunday

July 31, 2016
**Calculus 1**

simplify the expression. cos(2 tan^-1 x)
*Thursday, August 27, 2015 by TayB*

**Calculus 1**

Find the exact value of each expression. (a) cot^-1(sqrt(3))
*Thursday, August 27, 2015 by TayB*

**Calculus 1**

Find the exact value of each expression. (a) tan(sec^−1 5) (b) sin(2sin^-1(5/13))
*Thursday, August 27, 2015 by TayB*

**AP Calculus**

Find each of the limits without a calculator. Use the limits as an aide to sketch the graph of f(x)= (x-2)/(|x|-2) for-10<_x<_10 and -6<_y<_6. Be sure to clearly indicate any asymptotes, holes or other important characteristics. lim x->∞ f(x)
*Wednesday, August 26, 2015 by Ana*

**Calculus**

True or false. 1. If f(x) has a vertical asymptote at x=a, then the limit of f(x) as x --> a from the left is negative infinite and the limit of f(x) as x--> a from the right is positive infinite. I think this is true. Take for instance, a rational function. the two ...
*Wednesday, August 26, 2015 by Anonymous*

**Calculus**

The equation of a circle, C, is x^2 + y^2 + 6x - 8y +9=0. Find the center of C and find the radius of C. Show that the C touches the x-axis. Find the equation of the circle which is a reflection of C in the y-axis
*Wednesday, August 26, 2015 by Sabrina*

**Calculus **

Derivatives - chain rule An airplane, flying horizontally at an altitude of 1 mile, passes directly over an observer. If the constant speed of the airplane is 400 miles per hour, how fast is its distance from the observer increasing 45 seconds later? Hint: note that in 45 ...
*Tuesday, August 25, 2015 by Ribie*

**Calculus **

Derivatives - chain rule An airplane, flying horizontally at an altitude of 1 mile, passes directly over an observer. If the constant speed of the airplane is 400 miles per hour, how fast is its distance from the observer increasing 45 seconds later? Hint: note that in 45 ...
*Tuesday, August 25, 2015 by Ribie*

**Calculus 1**

Use a graph to estimate the values of x such that e^x > 1,000,000,000
*Monday, August 24, 2015 by TayB*

**calculus**

find the two numbers whose sum is 10, if the product of one by the cube of other is a maximum.
*Monday, August 24, 2015 by jen *

**Calculus **

If 2 < or = to f(x) < or = to x^2 + 2 for all x, find the limit of f(x) as it approaches zero.
*Sunday, August 23, 2015 by Anonymous*

**Calculus **

F(x)=(2x-1)/ (|x| -3) Rewrite f(x) as a piecewise function. Then find the limit as it approaches positive infinity and negative infinity.
*Sunday, August 23, 2015 by Anonymous*

**Differential calculus**

A gutter with trapezoidal cross section is to be made from a long sheet of tin 8 in wide by turning up one third of its width on each side , what width a cross the top that will give a maximum capacity
*Sunday, August 23, 2015 by Grace*

**calculus**

y=2^nx differentiate with respect to x using the first principle
*Sunday, August 23, 2015 by edward*

**Calculus **

If 2 < or = to f(x) < or = to x^2 + 2 for all x, find the limit of f(x) as it approaches zero.
*Sunday, August 23, 2015 by Anonymous*

**Calculus **

F(x)=(2x-1)/ (|x| -3) Rewrite f(x) as a piecewise function. Then find the limit as it approaches positive infinity and negative infinity.
*Sunday, August 23, 2015 by Anonymous*

**calculus: don't even no where to start from need help plz**

(1)find dy/dx of y if y=tan^(-1)1/x^2 (2) if y=3z^2.z^2 find dy/dz (3) if y=x^x show that dy/dx=x|n(x+1).. thanks
*Sunday, August 23, 2015 by edward*

**Calculus **

Find the limit as it approaches zero. ( f( x + change in x) - f(x) )/ change in x given f(x)=2x-5. ( change in x = triangle x)
*Sunday, August 23, 2015 by Anonymous*

**Calculus **

Graph the function f(x)= x sin( 1/x) and the equations y=|x| and y=-|x| in the same viewing window on your calculator. Then use the squeeze therom to find the limit of f(x) as it approaches zero. I graphed the function and equations, but I am confused on how to find the limit ...
*Sunday, August 23, 2015 by Anonymous*

**Calculus**

What would the limit be for the following problems? lim (square root (x+3)) x--> 1 I thought it would be 1.4 lim (1/x) x--> 7 I thought it would be 0 or .1 but neither of those show to be correct. Thank you!
*Saturday, August 22, 2015 by Serena*

**Calculus 1**

A variable star is one whose brightness alternately increases and decreases. For one such star, the time between periods of maximum brightness is 4.7 days, the average brightness (or magnitude) of the star is 5.3, and its brightness varies by ±0.35 magnitude. Find a ...
*Saturday, August 22, 2015 by TayB*

**Calculus**

A line rotates in a horizontal plane according to the equation Y = 2t^3- 6t, where Y is the angular position of the rotating line, in radians, and t is the time, in seconds. Determine the angular acceleration when t = 2 sec.
*Saturday, August 22, 2015 by Linda*

**PLEASE HELP WITH CALCULUS 1 - ITS REALLY URGENT **

Velocities of the 2 cars during the race are given in the tables below where velocities, v are in miles per hour and times t are in seconds. Sappho's car: time: 0 1 2 3 4 5 6 7 8 9 10 velocity:0 20 35 48 62 75 85 93 99 106 111 Homer's car: time: 0 1 2 3 4 5 6 7 8 9 10 ...
*Friday, August 21, 2015 by Ashley*

**Calculus 1**

Evaluate the difference quotient for the given function. Simplify your answer. f(x) = 1+2x− x^2, (f(4+h)-f(4))/h
*Thursday, August 20, 2015 by TayB*

**Calculus 1**

Find f o g o h. f(x) = x + 9, g(x) = 3x, h(x) = x − 5
*Thursday, August 20, 2015 by TayB*

**Calculus 1**

Explain how the following graphs are obtained from the graph of y=f(x). (Select all that apply.) (d) y= -2f(x) shift 2 units upward shift 2 units downward shift 2 units to the right shift 2 units to the left stretch the graph vertically by a factor of 2 shrink the graph ...
*Thursday, August 20, 2015 by TayB*

**Calculus 1**

Explain how the following graphs are obtained from the graph of y=f(x). (Select all that apply.) (a) y=7f(x) shifts 7 units upward shifts 7 units downward shifts 7 units to the right shifts 7 units to the left stretch the graph vertically by a factor of 7 shrink the graph ...
*Thursday, August 20, 2015 by TayB*

**Calculus - HELP URGENT PLEASE**

Consider a lake of constant volume 12200 km^3, which at time t contains an amount y(t) tons of pollutant evenly distributed throughout the lake with a concentration y(t)/12200 tons/km^3. assume that fresh water enters the lake at a rate of 67.1 km^3/yr, and that water leaves ...
*Thursday, August 20, 2015 by Ashley*

**Calculus **

(3x |x-2|) / x-2 What is the limit as x approaches 2 from the left side?
*Wednesday, August 19, 2015 by Anonymous*

**Pre-Calculus**

How do I solve these equations? I need to create an equation given the characteristics? I have to be able to graph a parabola but first I need help solving this. 1.Focus (1.5,1); opens right; directrix x=0.5 2.Focus (1,4);opens down; contains (-3,1)
*Wednesday, August 19, 2015 by Stephanie*

**Calculus 1**

Find an expression for a cubic function f if f(1)=8 and f(-1)=f(0)=f(2)=0
*Wednesday, August 19, 2015 by TayB*

**Calculus **

(2x + sin x)/x What is the limit as x approaches zero?
*Wednesday, August 19, 2015 by Anonymous*

**Diff Calculus**

a swimming pool is 5m wide, 10m long, 1m deep at the shallow end, and 3 m deep at its deepest point. a cross section is shown in the figure. if the pool is being filled at a rate of 0.1 m3/min, how fast is the water level rising when the depth at the deepest point is 1m?
*Tuesday, August 18, 2015 by Gene*

**Calculus 1**

A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 18 in. by 30 in. by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume V of the box as a function of x.
*Tuesday, August 18, 2015 by TayB*

**Calculus 1**

A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 32 ft, express the area A of the window as a function of the width x of the window.
*Tuesday, August 18, 2015 by TayB*

**Calculus **

Hello, Could somebody kindly check my answer for the following question? Find the derivative of the following function: h(x)=3e^(sin(x+2)) h'(x)=3'(e^(sin(x+2))+3(e^(sin(x+2))' h'(x)=0(e^(sin(x+2))+3(e^(sin(x+2))(cos(1)) h'(x)=3cos1(e^(sin(x+2...
*Tuesday, August 18, 2015 by Constantine*

**Math (Calculus)**

Hello, I have a difficulty with the following question. The question is asking to find the slope of the tangent at x=3 for this function: f(x)=4x^3/sinx. X is measured in radians. The is the derivative of f(x): f'(x)=(12x^2)(sinx)^-1 + (4x^3)(-1)(sinx)^-2(cosx) When x=3 is...
*Tuesday, August 18, 2015 by Constantine*

**calculus**

find the minimum and maximum points of the curve y=x^4-4x^3+4x^2
*Tuesday, August 18, 2015 by leo*

**Maths- calculus**

You are at a point x=x(t) along a horizontal line, representing the ground. You are flying a kite which maintains a constant height of 40 meters. Assume also that the kite string is a straight line. The kite is above the point k=k(t) on the ground, which is currently 30 meters...
*Sunday, August 16, 2015 by Kritish*

**Calculus **

As x goes to zero, what is the limit of (( 1/ x+2) -(1/2)) / x? I know the answer is -1/4, but I'm confused on how to get that answer. I think I have to multiply by the reciprocal.
*Saturday, August 15, 2015 by Anonymous*

**pre-calculus urgent**

Please help me here as well to clarify more my understanding. Let a1, a2, a3, . . . be a geometric sequence with initial term a and common ratio r. Show that a1^2, a2^2, a3^2, . . . is also a geometric sequence by finding its common ratio. Given that the ratio for a1, a2, a3...
*Saturday, August 15, 2015 by Alex*

**pre-calculus urgent**

The first term of an arithmetic sequence is 6, and the tenth term is 2. (a) Find the common difference d. d = Find the 100th term of the sequence. a100 = (b) Find the partial sum of the first ten terms. S10 = how do i do this, there's an example I tried following but it ...
*Saturday, August 15, 2015 by Alex*

**Pre-Calculus**

A local salesman receives a base salary of 675 monthly. He Also receives a commission of 11% on all sales over 1900. How Much would he have to sell in a month if he needed to have a monthly income of 3000? My Work: 1900*.11=209 3000-675=2325 2325/209=11.12440191 1900*11....
*Friday, August 14, 2015 by Lost*

**Calculus**

The following rational function describes concentration in blood of a certain medicine taken once depending on time, find: A) the horizontal or oblique asymptote B) the vertical asymptote, if any C) describe their meanings f(x)=x/x^2-100
*Friday, August 14, 2015 by Wendy*

**Calculus**

Posted by hey on Monday, August 10, 2015 at 11:28pm. A man 5.5 ft tall walks away from a lamp post 10 ft high at the rate of 8 ft/s. (a.) How fast does his shadow lengthen? (b.) how fast does the tip of the shadow move? Calculus - Reiny, Monday, August 10, 2015 at 11:43pm make...
*Wednesday, August 12, 2015 by hey*

**Math (Calculus)**

Hello, Could somebody please help me with the following question? It asks to differentiate the function below according to derivate rules of calculus such as the power rule (if f(x)=x^n, then f'(x)=nx^n-1), the product rule (if F(x)=f(x)g(x) then F'(x)=f(x)g'(x)+f...
*Wednesday, August 12, 2015 by Constantine*

**calculus**

A person is jumping straight up and down on a trampoline. The height of the center of mass of the person is measured every tenth of a second. It takes just over one second to complete one full bounce. (If you want to see the data, look at the video above.) t (seconds) 2.90 3....
*Wednesday, August 12, 2015 by JuanPro*

**calculus**

This problem requires a calculator. Enter answers as decimals. Grass clippings are placed in a bin, where they decompose. The amount of grass clippings measured in kilograms is modeled by A(t)=7.0(0.95)t, where t is measured in days. (a) Find the average rate of change of A(t...
*Wednesday, August 12, 2015 by JuanPro*

**calculus**

F. (12) (1 punto posible) You are at a point x=x(t) along a horizontal line, representing the ground. You are flying a kite which maintains a constant height of 40 meters. Assume also that the kite string is a straight line. The kite is above the point k=k(t) on the ground, ...
*Wednesday, August 12, 2015 by JuanPro*

**calculus**

F. (11) (2 puntos posibles) Consider a circular cone with base of radius a and a height of a. Find the vertical cylinder of largest volume inside this cone. In terms of a, what is the radius of this largest cylinder? (Enter ∗ for multiplication: type 2*x for 2x. Enter...
*Wednesday, August 12, 2015 by JuanPro*

**calculus**

You are given that f(x) =1+ax+ax2 f′(x) =−(x+2)ax3 f′′(x) =(2x+6)ax4 and the constant a>0. Write down all intervals on which the function is increasing, decreasing, concave up or concave down. (Enter using notation (a, b). Use a comma to separate ...
*Wednesday, August 12, 2015 by JuanPro*

**calculus**

(a) Give the linear approximation for the function e−x1+x near x=0. (Enter ∗ for multiplication: type 2*x for 2x. Enter / for division: type 1/2 for 12.) - sin responder (b) Give the quadratic approximation for the function ln(cosx) near x=0. (Enter ∗ for ...
*Wednesday, August 12, 2015 by JuanPro*

**calculus**

F. (7) (2 puntos posibles) Let f(x)={tanxax+bπ/4<x<π/2x≤π/4 Find a and b such that the function f(x) is differentiable at x=π/4.
*Wednesday, August 12, 2015 by JuanPro*

**calculus**

Evaluate these limits. (Enter answer as a decimal. Enter INF if the limit is +∞; -INF if the limit is −∞; and DNE if the limit is neither ±∞ and does not exist.) (a) limx→04+x−−−W22;−√−2x= - ...
*Wednesday, August 12, 2015 by JuanPro*

**calculus**

Draw the graph of the function (qualitatively accurate). y=x+1−−−−−√/(x−b),1<b<2
*Wednesday, August 12, 2015 by JuanPro*

**calculus**

Find the tangent line to the curve xy3+2y−2x=1 through the point (x,y)=(1,1). (Enter ∗ for multiplication: type 2*x for 2x. Enter / for division: type 1/2 for 12.) Tangent Line y=
*Wednesday, August 12, 2015 by JuanPro*

**calculus**

F.(0) (10 puntos posibles) C1 What is limh→0cos(π6+h)−cos( 60;6)h? (Enter the answer as a decimal. If the limit does not exist, enter DNE.) sin responder Loading C2 At which of the five points on the graph are dydx and d2ydx2 both ...
*Wednesday, August 12, 2015 by JuanPro*

**Calculus**

The balloon leaves the ground 80 ft. from an observer and rises vertically upward at 5 ft/s. (a) How fast is the balloon receding from the observer after 12 seconds? (b) find the corresponding acceleration? How do I sketch it? and what equation should I use? Please show the ...
*Wednesday, August 12, 2015 by Jean*

**Calculus**

A man 5.5 ft tall walks away from a lamp post 10 ft high at the rate of 8 ft/s. (a) How fast does his shadow lengthen? (b) How fast does the tip of the shadow move? Can you please tell me what method/s you used to come up with a solution? I wasn't sure about the sketch I ...
*Wednesday, August 12, 2015 by Jean*

**Calculus **

Differentiate this y = 1 - cos^2 x
*Tuesday, August 11, 2015 by Ribie*

**calculus**

A particle p moves in a straight line with a velocity v m/sec that is given by v=4t^2-1 where t is the time after passing through a fixed point O on the line .find the instant when p is instantaneously at rest .also find at that instant ,displacement of p from O.
*Tuesday, August 11, 2015 by raheel khan*

**Calculus **

Differentiate this y = 1 - cos^2 x
*Tuesday, August 11, 2015 by Ribie*

**Calculus**

A man 5.5 ft tall walks away from a lamp post 10 ft high at the rate of 8 ft/s. (a.) How fast does his shadow lengthen? (b.) how fast does the tip of the shadow move?
*Monday, August 10, 2015 by hey*

**Calculus**

Y = 1 - cos^2 x
*Monday, August 10, 2015 by Ribie*

**calculus**

find the equation of the curve for which y'''=24x-6 if the curve passes through (-1,8) and is tangent to the line y=4x at (1,4). help please thanks :-)
*Monday, August 10, 2015 by jean*

**calculus**

find the equation of the curve for which y''=(12/x^3) if it passes through (1,0) and is tangent to the line 6x+y=6 at that point.
*Monday, August 10, 2015 by justin*

**calculus**

find the equation of a curve for which y''=6x-6 if the curve has a critical point at (2,1).
*Monday, August 10, 2015 by justin*

**pre-calculus**

two gears are connected by a belt. the large gear has a radius of 20cm while the small gear has a radius of 10cm. if a point on the small gear travels at 16 rpm (revolutions per minute), find the angular velocity of the large gear. Tip: first find the velocity of the belt
*Monday, August 10, 2015 by Mack*

**calculus**

find the equation of the curve for which y''=6x-4 and which passes through (1,2) and (-2,5).
*Monday, August 10, 2015 by justin*

**calculus**

find the equation of the curve for which y'=3x^2 and which passes through (1,-1)
*Monday, August 10, 2015 by justin*

**Calculus**

Y = 1 - cos^2 x
*Monday, August 10, 2015 by Ribie*

**calculus**

if the driver of a car wishes to increase his speed from 20 mph to 50 mph while traveling a distance of 528 ft., what constant acceleration should he maintain?
*Monday, August 10, 2015 by jean*

**calculus**

a particle starts from rest and moves along a straight line with an acceleration equal to 24-15√t where distance and time are measured in terms of feet and seconds respectively. with what acceleration will the particle return to the starting point? help please thank you :-)
*Monday, August 10, 2015 by jean*

**calculus**

a stone dropped from a balloon which was rising at the rate of 15 ft./sec. reached the ground in 8 seconds. how high was the balloon when the stone was dropped?
*Monday, August 10, 2015 by jean*

**Calculus - HELP URGENT PLEASE**

The region R is bounded by the x-axis, x=2 and y=x^2. Which of these expressions represents the volume of the solid formed by revolving R about the line x=2?
*Sunday, August 9, 2015 by Ashley*

**Calculus 1**

Find the volume of the solid obtained by rotating the region under the graph of the function f(x)=2x+1 about the x-axis over the interval [0,1]. I have no clue how to start this..... :(
*Thursday, August 6, 2015 by Luke*

**calculus**

If the driver of a car wishes to increase his speed from 20 mph to 50 mph while traveling a distance of 528 ft., what constant acceleration should he maintain?
*Thursday, August 6, 2015 by jean*

**calculus**

a particle starts from rest and moves along a straight line with an acceleration equal to 24-15√t where distance and time are measured in terms of feet and seconds respectively. with what acceleration will the particle return to the starting point?
*Thursday, August 6, 2015 by jean*

**calculus**

A stone dropped from a ballon which was rising at the rate of 15 ft./sec. reached the ground in 8 seconds. how high was the ballon when the stone was dropped? please help :-) thank you
*Thursday, August 6, 2015 by jean*

**calculus**

Find the equation of the curve for which y''=6x-4 and which passes through (1,2) and (-2,5). thank you :-)
*Thursday, August 6, 2015 by justin*

**calculus**

Find the equation of the curve for which y'=3x² and which passes through (1,-1).
*Thursday, August 6, 2015 by justin*

**Calculus**

I have the question :A small blood vessel of radius 2mm branches off at an angle(theta) from a larger blood vessel of radius 4mm. According to Poiseuille's Law the total resistance to the blood flow is proportional to T=(a-bcot(theta)/4^4)+(bcsc(theta)/2^4) Show that the ...
*Thursday, August 6, 2015 by Jessica*

**calculus**

If dy=(2x+1)dx and y=7 when x=1, find the value of y when x=3.
*Thursday, August 6, 2015 by justin*

**Calculus**

My question is:Use L'Hospital's rule to find limit as x approaches 0 (e^x-e^-x-2x)/x-sinx. 1st I took the derivative to get (e^x-e^-x-2)/1+cosx. Substituting in 0, I got -1. The answer is supposed to be 2.I also tried (e^x-xe^-x-2)/1+cosx, and wound up with -(1/2). I ...
*Thursday, August 6, 2015 by Jessica*

**Calculus**

Can someone show how to solve this problem Find the equation of the tangent line to the curve given by, x=3e^t y=5e^-t at the point where t=0 Thanks!
*Wednesday, August 5, 2015 by Henry*

**Calculus**

Can someone show how to solve this problem Find the equation of the line normal to the graph of y = x^2 + 1 that passes through the point (1, 2). Thanks!
*Wednesday, August 5, 2015 by Henry*

**Calculus**

Find the area bounded by the y-axis and x = 4-y^2/3 Thanks!
*Tuesday, August 4, 2015 by Gela*

**Calculus**

The area bounded by the curve y^2 = 12x and the line x=3 is revolved about the line x=3. What is the volume generated?
*Tuesday, August 4, 2015 by Gela*

**calculus**

a parachutist falling at the rate of 15 ft./sec. drops a stone. if he was 904 ft. above the ground when the stone was dropped, how long would it take the stone to reach the ground?
*Tuesday, August 4, 2015 by jean*

**calculus**

a particle moves according to the law a=1/t √t. if s=8 when t=1. and s=16 when t=4. find v when t=9.
*Tuesday, August 4, 2015 by jean*

**Calculus**

The region in the first quadrant bounded by the x-axis, the line x = ln(π), and the curve y = sin(ex) is rotated about the x-axis. What is the volume of the generated solid? Got 2.8 and .79 very confused
*Tuesday, August 4, 2015 by Ali*

**Calculus**

Please help simplify this expression: 2 log (base 4) ^9 - log (base 2) ^3 The answer should be log(base 2) ^3
*Tuesday, August 4, 2015 by Alisha*

**Calculus**

Find the area bounded by the y-axis and x = 4-y^2/3
*Tuesday, August 4, 2015 by Rose*

**Calculus **

(1-sin^2 theta) - (sin^2 theta) (1-sin^2 theta) * (sin^2 theta)
*Thursday, July 30, 2015 by Seany*

**Calculus - Rate of Change**

Can someone explain how to solve this problem? Sand is being dumped on a conveyor belt onto a pile in such a way that the pile forms in the shape of a cone whose radius is always equal to its height. Assuming that the sand is being dumped at a rate of 10 cubic feet per minute...
*Wednesday, July 29, 2015 by Fred*

**Calculus**

An airplane is heading at a bearing of N23°E at a speed of 700 km/hr, but there is a wind blowing from the west at 60 km/hr. If the plane does not make any correction, what will be the bearing of the plane? What is its speed relative to the ground (ground speed = airspeed...
*Wednesday, July 29, 2015 by Alexa*

**calculus**

what is the interval notation for solution set of the inequality x^2+16x is less than or equal to 0
*Wednesday, July 29, 2015 by Hazel*

**Calculus**

The base of a solid in the first quadrant of the xy plane is a right triangle bounded by the coordinate axes and the line x + y = 2. Cross sections of the solid perpendicular to the base are squares. What is the volume, in cubic units, of the solid?
*Tuesday, July 28, 2015 by Ali*

**Calculus**

Can someone show how to solve this problem Two vertical towers of heights 60 ft and 80 ft stand on level ground, with their bases 100 ft apart. A cable that is stretched from the top of one pole to some point on the ground between the poles, and then to the top of the other ...
*Monday, July 27, 2015 by Hank*

**pre-calculus **

which expression is equivalent to (sinx+1)(sinx-1)? A.) COS^2X B.) -COS^2X C.) COS^2X+1 D.) COS^2X-1 E.) -COS^2X+1
*Monday, July 27, 2015 by Daisy*