# Calculus

**Pre-Calculus**

a jet, in calm air conditions, travel with velocity vector (389, 389). the wind velocity (in mph) at the plane's cruising altitude is given by (0, 50). how fast is the plane's true speed

**Calculus**

Find the magnitude and direction angle of p=42i+35j

**Calculus**

Find the magnitude and direction angle of p=42i+35j

**Calculus**

For which values of x does the curve Y= (3x^3-3x^2+1) / (2x^2-1) , have a horizontal tangent? Show steps or explain, i dont get it

**Calculus**

Comute f(x) of a) f(x) = sinxcosx / sinx + cosx b) f(x) = (1-x^2) / (1+x+x^2) c) f(x) = x^7 secx

**Calculus**

Knowing that F(-2) = -7, F'(-2)= 12, g(-2)= -3 and g'(-2)= -9, Compute: a) h'(-2) if h(x)= f(x)g(x) b) h'(-2) if h(x) = f(x) / g(x) c) h'(-2) if h(x) = g(x) / 1+(f(x))^2 Show all steps

**Calculus**

Let F(x) = (x+1) / (x^2-16). Use the definition of the derivative to compute f'(x) and give its domain. Show all steps.

**Calculus**

A population of 1200 badgers grow by 6% every 8 years. How long does it take the population of badgers to grow 2000?

**calculus**

Find the volume of a solid whose base is bounded by the parabola x=y^2 and the line x=9, having square cross-sections when sliced perpendicular to the x-axis.

**Calculus**

Write an expanded polynomial equation based on the following information. A cubic function with a zero x=3 (with multiplicity 2), a zero at x=2, and a constant term of 18.

**calculus**

limx--->3- 5/x-3 I think it is -inf but I don't know how to prove it

**calculus**

A student throws a ball upward from a height of 48ft, initially at 32ft per second. What is the maximum height of the ball?

**calculus**

if limit x--->0(4-g(x)/x)=1

**calculus**

limx--->0 3sin 3x/4x would it be 9/4

**Help! Calculus**

I am so confused on how to solve this problem. I have it set up with y's on one side and x's on the other but I don't know what to do from there. Question: Solve the differential equation. The initial condition is y(0) = 1. ((x^2+1)^(1/2))(dy/dx) - (x/(2y)) = 0 y > 0 My ...

**calculus**

limx-->3 sin 3x/4x

**calculus**

find the average rate of change of the function f(x)=x^3+1 over the interval [-1,1]

**calculus**

Argus Company makes three products: A, B, and C. Each unit of A costs $4, each unit of B costs $2, and each unit of C costs $1 to produce. Argus must produce at least 20 As, 30 Bs, and 40 Cs, and cannot produce fewer than 200 total units of As, Bs, ...

**calculus**

if limx-->0(4-g(x)/x=1find limx--->0g(x)

**calculus**

find the limit x-->inf (x^2+x)^1/2-(x^2-x)^1/2 so I know I multiply by the conjugate 2x/(x^2+x)^1/2+(x^2-x)^1/2 then I don't know where to finish problem

**Calculus**

True or False,... Im confused If the continuous function f(x) has a domain (-∞, +∞), then either lim --> ∞ exists, or limit X--> ∞ is +-∞

**basic calculus**

x^3+x^2y+2y^2=0

**basic calculus**

x^3+x^2y+2y^2

**basic calculus**

find a appropriate formula for the area of a narrow circular ring....wedding band made of circular wire

**basic calculus**

find a appropriate formula for the area of a narrow circular ring

**Calculus AB**

What's the lim(x-->-infinity) sqrt(x^4-1)/(x^3-1)? I've tried solving for it but I got -1/0, which would make it undefined. Is that correct?

**Calculus AB**

So the problem is "For x>0, d(lnx)/dx = 1/x and lne=1. A) find the tangent line approximation for ln 3 B) calculate the %error in approximation in part A. My teacher said the answer for part A is that 1/e, and I'm pretty confused. So far I the given info into point slope ...

**Pre-Calculus**

How to solve sin(x/2) = 1 - cos x? I know you would use the half angle identity sin(x/2) = +-(√1 - cos x/2), just don't know what to do from there.

**Pre-Calculus**

How to solve sin(x/2) = 1 - cos x? I know you would use the half angle identity sin(x/2) = +-(√1 - cos x/2), just don't know what to do from there.

**Calculus II**

Sketch the region R defined by 1 ≤ x ≤ 2 and 0 ≤ y ≤ 1/x3. a) Find (exactly) the number a such that the line x = a divides R into two parts of equal area b) Then find (to 3 places) the number b such that the line y = b divides R into two parts of equal area

**applied calculus**

From a height of 25 meters a ball is thrown vertically upwards at a velocity of 5 meters per second. a.What time in seconds will the ball reach its maximum height? b.What is its maximum height? c.When will the ball strike the ground? d.What will be the ballâ€™s velocity ...

**Calculus**

I am having trouble with this question and I am unsure how to solve it... True or False (with justification) The function sin(x) if x ≤ 0 f(x) = 1+cos(x) if x>0 has a jump discontinuity at x = 0.

**calculus**

I have a definition lim theta approaching 0 sin theta/theta = 1 so show if the limit x approaching 0 sin2x/5=2/5

**calculus**

define f(x)={x+a if x>2 {-1 if x=2 {ax+b if x<2. How to determine the values of a and b for which f(x) is continuous in the set of real numbers.

**calculus**

Define h(x)={x^2 if x>=-1 {ax+b if x<-1 If f(-2)=-1, how do i determine the values of a and b for which h(x) is continuous in the set of real numbers

**calculus**

Let g(x)={x^2-x-2 if x is not equal to 1 {0 if x=1

**Calculus can you please show me the step by step s**

The intensity of light varies inversely as the square of the distance from its source. If two searchlights are 600 meters apart and one light is 8 times as strong as the other, where should a man cross the line between them in order to be illuminated as little as possible

**Calculus**

The intensity of light varies inversely as the square of the distance from its source. If two searchlights are 600 meters apart and one light is 8 times as strong as the other, where should a man cross the line between them in order to be illuminated as little as possible

**basic calculus**

The area of the surface of a sphere of radius r is 4πr^2. If the estimate radius of a spherical balloon is 200 meter and this estimate is too small by 1/2 meter. Find the approximate surface area in sq. m.

**calculus**

A stone thrown up from the top of a building with a velocity of 48 meter per second reaches the ground with a velocity of -50 m/s. Find the height of the building. Using the derivative of approximation.

**Calculus**

Find the vertical translation of y=|x| that "supports" the parabola y = x^2. Hint: You should find 'c' so that y = |x|+c just touches y = x^2. You may as well consider only the right-hand side of the picture first. (Why?)

**Applied Calculus**

From a height of 25 meters a ball is thrown vertically upwards at a velocity of 5 meters per second. a. What time in seconds will the ball reach its maximum height? b. What is its maximum height? c. When will the ball strike the ground? d. What will be the ball’s velocity ...

**Calculus**

Let A denote the portion of the curve y = sqrt(x) that is between the lines x = 1 and x = 4. 1) Set up, don't evaluate, 2 integrals, one in the variable x and one in the variable y, for the length of A. My Work: for x: âˆ«[4,1] sqrt(1+(dy/dx)^2) dy/dx = 1/2sqrt(x) (dy/dx)^2...

**calculus**

find the limit without using L'Hopital's Rule Lim(X->-4) (16-x^2 / x+4)

**Calculus**

Knowing that Pi/2 < x < Pi and that 0<y< Pi/2 that sinx = 1/5 and that cos y = 1/8, find sin (x+y), sin (x-y), cos (x+y) and cos (x-y). Explain.

**calculus**

Use implicit differentiation to find an equation of the tangent line to the curve 3xy^3+4xy=63 at the point (9,1)(9,1).

**calculus**

A spherical balloon is inflated so that its volume is increasing at the rate of 3.2 ft3/min. How rapidly is the diameter of the balloon increasing when the diameter is 1.1 feet?

**Calculus**

Find two non-intersecting intervals where f(x) +12x^4 + 50x^3 + 80x^2-100 has at least one root. Justify your answer.

**Calculus**

Compute F'(-4) where F(x) = x^3 + X^2 (using the definition of the derivative)

**Calculus**

Find all the values of (x) in the interval [0, 2Pi], such that sec^2 (x) = 4

**Calculus**

A manufacturer buys $280,000 worth of machinery that depreciates linearly so that its trade-in value after 10 years will be $30,000. Express the value of the machinery (V) as a function of its age (t).

**Calculus**

y = 2 cos(5πx) .... whats the period?

**Calculus**

Find the equation in standard form for the line that satisfies the given requirements. horizontal line through (−8, −9)

**Calculus**

Piecewise function x if −2≤x≤0; x^2 if −2<x<0; 8-x. If if −2≤x≤3; (d) Write down an analytic formula for f^{-1}, and state its domain and range.

**Calculus**

Solve the quadratic equation by factoring. (Enter your answers as a comma-separated list.) 5x2 − 23x = −12

**Calculus**

Can you please check to see if these answers are correct? I have provided my work as well! That you! This is much appreciated!! 1. What is the volume of the solid that is generated by revolving the region bounded by the curves x = 3y^2-2 and x = y^2 and y = 0 about the x axis...

**Pre-Calculus**

The base of the fish tank below has a length of 40 inches, a width of 20 inches, and height of 1.5 feet. The tank starts off with a water depth of 7 inches. You then add water to the tank at a constant rate such that the water level increases 1 inch every 2 minutes. Wirte a ...

**Calculus**

Find inverse equation of y= 3e^(x-1)^5 Answer I got is (ln(x/3))^(1/5) +5 =y But I think it's wrong because the domain and range is really different from the original equation

**calculus**

A 17- foot ladder is leaning against a wall, and begins to slide. The top of the ladder is falling at a rate of 2 feet per second at the instant that the bottom of the ladder is 8 feet from the wall. What is the rate of change of the distance between the bottom of the ladder ...

**calculus**

The mechanics at lincoln automotive are reboring a 6-in. deep cylinder to fit a new piston. The machine they are using increases the cylinder's radius 0.02 inches each second. How rapidly is the cylinder volume increasing when the bore (diameter) is 3.8 in.?

**calculus**

Melissa wants to make a rectangular box with a square base and cover its top and bottom faces with velvet, which will cost her $3 per square inch, and the sides with silk, which will cost her $5 per square inch. The box should have a volume of 1600 cubic inches. Find the ...

**Calculus**

Does F(x)=9-x^2 satisfy the hypothesis of the mean value theorem on the interval [0,3]? if it does, then find the exact values of all Ce(0,3) that satisfy the conclusion of the Mean Value Theorem.

**Calculus**

Consider the function f(x) = -3x+2. Notice the limit of f(x) as x approaches 1 is -1. Find a value for delta such that is the distance x is from 1 is less than delta, then the distance from f(x) to -1 is less than 0.05

**maths calculus also**

what is the area enclosed by the curved y=4x-x^2,and y=x^2-2x along the x-axis thanks so much help

**maths help calculus**

the area of a circle increasing at the rate of 3cm/sec.find the rate of change of the circumference when the radius is 2cm help plz

**Calculus**

Hello, I would like to make sure the answers to these questions are correct. 1. Using the shell method, what is the volume of a solid that is generated by rotating the region by y = x^2 and x = y^2 about the x axis. My Work: r = y h = sqrt(y) - y^2 2pi ∫[0,1] (y)((sqrt(y) - ...

**calculus**

how do you find the derivative of this (-x^2)/ (2) +2 and does it have any x intercepts, asypmtotes, or holes.

**Calculus**

How do you fine the derivative of (x-3)^-3

**Pre-Calculus**

sketch f(x) such that f(x) is increasing on (-inf,-2) and f is decreasing on (-2,0), f(x) has point discontinuity at x=-2, f(x) has a horizontal asymptote of y=4, f(x) is an odd function.

**Calculus Answer Check**

A particle moves along a line so that its position at any time t >= 0 is given by the function -t^3 + t^2 + 5t + 3, where p is measured in feet and t is measured in seconds. 1. Find the displacement during the first four seconds. My answer: 75 ft 2. Find the average ...

**Calculus algebra review**

((1/2+h) -(1/2)) / h found LCD of numerator ((2)-(2+h)/2(2+h))/h is it 1

**Calculus (Sequences)**

Hello, here is a picture of the question I am trying to solve, I believe the answer to be C, but I would just like some confirmation/correction. goo. gl/gWfhVn

**AP Calculus**

Consider the function f(x) = 1/4x^4 - 5/3x^3 - 3/2x^2 + 15x - 3. A. Find the relative extrema for f(x); be sure to label each as a maximum or minimum. You do not need to find function values; just find the x-values. B. Determine the interval(s) where f(x) is increasing (if any...

**Calculus**

I would like to make sure my answer is correct: Question: the base of a solid is the triangular region with the vertices (0,0), (2,0), and (0,4). Cross sections perpendicular to the x-axis are semicircles. Find the volume of this solid. My Work: ∫[0,2] (pi/2)(r^2)dx r = (-2x...

**calculus**

Find the values for the following functions. If f(x)=2^x, show that f(x+3) -f (x-1)=15/2f(x) If G(x)= sin 2x, find G(0),G(1/4 pie),and G(7/8 pie)

**calculus**

Find the domain of the variable x for which the following equations determine y as a real function of x. If G(x)= sin 2x, find G(0),G(1/4 pie),and G(7/8 pie) can someone help me please!

**Vector Calculus**

Can someone help me with this please. A vector field in cylindrical polar co-ordinates is given by V = R Rˆ + R 3 s i n ( φ ) c o s ( φ ) φˆ + 3 z kˆ where Rˆ, φˆ, kˆ are the appropriate unit vectors. Translate this vector field into the Cartesian x, y, z co-ordinate...

**Calculus**

I would like to know if my answers are correct: Disclaimer: We are allowed to keep our answers in formula form 1. Use the washer method to find the volume of the solid that is generated by rotating the plane region bounded by y=x^2 and y = 2-x^2 about the axis y=-1 My Work: [...

**calculus**

Find the domain of the variable x for which the following equation determine y as a real function of x. y - xy = 5

**vector calculus**

Can someone help me with this please. A vector field in cylindrical polar co-ordinates is given by V = R Rˆ + R 3 s i n ( φ ) c o s ( φ ) φˆ + 3 z kˆ where Rˆ, φˆ, kˆ are the appropriate unit vectors. Translate this vector field into the Cartesian x, y, z co-ordinate...

**Applied calculus**

A rectangular plot requires 2000 m of fencing to enclose it. If one of the dimensions is x meters, express the area y (m2) as a function of x. Determine the range of x.

**Calculus**

From each corner of a square of tin, 12 cm on a side, small squares of side x are removed and the edges are turned up to form an open box. Express the volume V (cm3) as a function of x. Determine the range of x.

**Calculus**

Find any critical numbers of the function f(Ø)= 2secØ +tanØ, 10π < Ø < 12π A. 67π/6 B. 71π/6 C. 63π/6 D. A and B

**Calculus**

Find the value of the derivative of the function f(x)=7-|X| at the extrema point (0,7)? A. Does not exist B. 0 C. 7 D. -7

**Calculus**

If f is differentiable at x=c, which of the following statements must be true? A. f is continuous at x=c B. f^1 is continuous at x=c^1 C. f is continuous at y=c D. f is continuous at y^1=c

**Calculus**

A surgical laser is cutting an incision in the eye according to the equation x^2-4y^2=9, y>0. The incision rates vary to allow for curvature of the eye. When x=5, dx/dt=300 manometers per second. What is dy/dt at that moment? A. 18.75 manometers per second B. 93.75 ...

**Calculus**

What is dy/dx given that xy^2-xy+x=y?

**Calculus**

Which of the following is written in explicit form? A.y=x B.x^2-6xy-9y^2=0 C.y=0 D. y= -√1-x^2

**Calculus**

What is the derivative of h(x)= 3x+2/x^2-5?

**Calculus**

What is dy/dx when y=(x^2 - 4x ) ^3 ? A. 3(x^2 -4x)^2 B. (6x - 12) (x^2 -4x)^2 C. 3(2x - 4)^2 D. 6x^2(2x-4)^2

**Calculus**

What is the derivative of k(x)=sin x cos x? A. -sin x cos x B. -2 sin x cos x C. 2 cos^2x-1 D. sin^2x - cos^2x

**Calculus**

If the position function in feet for a free-falling particle on Planet X is s(t)= -8t^2 +16 + 64, what is the velocity of the after 2 seconds in feet per second? A. -32 B. -16 C. 16 D. 64

**Calculus**

From each corner of a square of tin, 12 cm on a side, small squares of side x are removed and the edges are turned up to form an open box. Express the volume V(cm3) as a function of x. Determine the range of x.

**Calculus**

f'(x)=sqrt(x)*sin(x) The first derivative of the function f is given above. If f(0)=0, at which value of x does the function f attain it's minimum value on the closed interval [0,10]? I know the answer is 6.28, but I need steps as to why. Please and thank you.

**PLEASE HELP BEEN STUCK ALL DAY CALCULUS**

The radius of a 12 inch right circular cylinder is measured to be 4 inches, but with a possible error of ±0.2 inch. What is the resulting possible error in the volume of the cylinder? Include units in your answer.

**Calculus Please Help**

The radius of a 12 inch right circular cylinder is measured to be 4 inches, but with a possible error of ±0.2 inch. What is the resulting possible error in the volume of the cylinder? Include units in your answer. my answer 30.16

**Calculus Please Help**

evaluate the table and find d/dx [g[f(2x)]] at x=1 f(x) 6,1,6,2 f'(x) 1,2,5,7 g(x) 1,4,4,3 g'(x) 4,5,5,-4

**Calculus**

Find the x-coordinates where f '(x) = 0 for f(x) = 2x + sin(2x) in the interval [0, 2π]. MY ANSWERS: x = π/2 x = 3π/2

**Calculus**

a 160-inch strip of metal 20 inches wide is to be made into a small open trough by bending up two sides on the long side , at right angles to the base. the sides will be the same height , x. if the tgrough is to have a maximum volume, how many inches should be turned up on ...

**Calculus**

The radius of a 12 inch right circular cylinder is measured to be 4 inches, but with a possible error of ±0.2 inch. What is the resulting possible error in the volume of the cylinder? Include units in your answer. V = πr²h = 16πr² dV/dr = 32πr dV = 16πr dr Let dV and dr...