# Calculus

Calculus
Determine the average rate of change of f(x)=1/(x^2 -x) over the interval 2 is less then or equal to x and 3 is greater or equal to x.

Pre-calculus
Evaluate sin16° cos29° + cos16° sin29°

Pre-calculus
Evaluate sin 7pi/12. Using sum, difference, and cofunction identities

Pre-calculus
Find the acute angle between the lines 2x-3y-6=0 and x+5y-20=0

Pre-calculus
Derive an identity that transforms sin(α+β+γ) into a sum of products of sines and/or cosines of the individual numbers α, β, γ.

Pre-calculus
If sin x=-3/5 and sec x>0, find all the other circular function values of x

Calculus
The percentage of research articles in a prominent journal written by researchers in the United States can be modeled by A(t) = 25 + (36/1 + 0.6(0.7)^−t'), where t is time in years (t = 0 represents 1983). Numerically estimate lim as t→+infinity A(t).

calculus
A spherical balloon is being inflated so at the rate of 8cm3/sec. determine the rate at which the radius of the balloon is changing when the radius is 10

Calculus
A ball is thrown vertically into the air so that its height s after t seconds is given by the equation, s=-1/27(t^2)+4√t. Find its maximum height.

Calculus
Find the volume of the solid under the plane 3x + 3y − z = 0 and above the region bounded by y = x and y = x^4

Calculus
Find the volume of the given solid. Under the surface z = 7xy and above the triangle with vertices (1, 1), (4, 1), and (1, 2)

Differential Calculus
A conical tank with height is 10 and radius is 5 is being filled with water at 4m^3/s. Solve how fast is the water when = 3m

Pre-Calculus
A hemispherical bowl with a 30-centimeter radius contains some water, which is 12 centimeters deep. Find the volume of the water.

Calculus I
y = x^3 - 8x^2 + 6x -2 has a slope of 6 at two points, what are the coordinates? I did the power rule to derive the equation: y'= 3x^2 - 8x + 6 , and then I tried to factor it to find the x intercepts but it doesn't work. But anyway, my point of confusion is where does the ...

Calculus
I want to know how to find the local linearization. So in this problem I'm doing, I'm given the f(x) equation and it says "about x = 0" I'm suppose to approximate value of f(0.3) Are there specific steps I need to take to go about this problem?

calculus
Find the slope of the tangent line to the curve (sqrt(4x+y))+(sqrt(3xy)) at the point (3,4) The slope of the tangent line to the curve at the given point is ? I got -((1/2)+4sqrt(36))/((1/8)+3sqrt(36))

Calculus
If x=2cos (z) and y= sin (z), then d^2y/dx^2=? What I got -sin (z) / -8cos (z)*sin (z) simplifies to 1/8cos (z) I don't think I'm right...

calculus
Use implicit differentiation to find the derivative of the family of curves sin(xy)+x5+y5=c. dy/dx=? I got (-5x^4-ycos(xy))/(xcos(xy)+5y^4)). what am I doing wrong? Help please

Calculus
an experimental farm has 3600 ft. of fencing to create a rectangular area that will be subdivided into 4 equal subregions, what is the largest total area that can be enclosed?

Calculus I
You are watching the Chicago marathon from your friend's apartment, 100 feet above the street. A runner passes the building at 11 feet/sec. Let d denote the distance between the base of the building and the runner, and let h denote the distance between you and the runner. How ...

Physics
Hello, I need that someone help me with this excersise. I have to calculate (USING INTEGRATION) the motion ecuation of a particle. The excersise give me the ecuation of the velocity that is v=14t-32 , the initial time t1=3 And the initial position of the particle: X1=25 My ...

Calculus, Related Rates
At 12 noon ship A is 60 miles west of point P steaming east at 15 knots and ship B is 36 miles south of P steaming north at 10 knots. If the ships continue their courses and speed. how is the distance between them changes at 2pm? At what time the ships are closest? The answers...

Calculus - Approximation
Use linear approximation, i.e. the tangent line, to approximate cubed root { 1.1 }. The equation of the tangent line to f(x) at x = 1 can be written in the form y = mx+b. Show your work. Do not use a calculator.

Calculus
find the extremum of f(x,y) subject to the given constraint, and state wether it is a maximum or minimum. 4y^2-29x^2; 3x+y=21

Math - Calculus 1
Approximate using derivatives. (Must show work using derivatives!) Do not use a calculator: (1.1)^4 - (1.1)^2

Calculus - Related Rates
Suppose that you are watching a spaceship take off. You are 100 meters from the launch pad, and you measure the angle made by the rocket and the ground to be increasing at a rate of (d)(theta)/dt = 0.1 radians per second. What is the velocity of the rocket when theta = pi/4?

Math - Calculus 1
Approximate the following value using derivatives (without a calculator) (1.1)^4 - (1.1)^2 I only know how to do linear approximation when using square roots. How do I do this type of problem?

calculus
use Simpson's with n=10 to approx. f(x)= x sin x, 0¡Ü x ¡Ü2¦Ð round to 6 decimal places I know I set up the calculation correctly like this: (pi/15)(f(0)+4f(pi/5)+2f(2pi/5)+...+2f(8​pi/5)+4f(9pi/5)+f(2pi) I keep getting a negative answer but I know that the answer ...

Calculus 1
Rick has 1200 feet of fence that he wants to use to enclose a rectangular garden. Find the maximum area the garden can have.

Pre-Calculus
Given Tan(A) = 5 in Quadrant III and Sin(B) = ⅔ in Quadrant II, find Cos(A-B).

Pre-Calculus
Given Sin(A) = ⅗ and Cos(B) = 8/17 in Quadrant I, find Cos(A+B).

Pre-Calculus
Given Sin(A) = ⅗ and Cos(B) = 8/17 in Quadrant I, find Sin(A+B).

calculus
find the minimum distance from the point (4,1) to the parabola y^2=4x.

calculus
12. (1 point) The height y (in feet) of a ball thrown by a child is y = − 1 16 x 2 +4x+5 where x is the horizontal distance in feet from the point at which the ball is thrown. (a) How high is the ball when it leaves the child’s hand? (b) What is the maximum height of ...

Pre-Calculus
A.Verify the identity. B.Determine if the identity is true for the given value of x. Explain. [cot(x) – 1] / [cot(x) + 1] = [1 – tan(x)] / [1 + tan(x)], x = π/4 I solved A and I believe it's true; however, I need help with B.

Pre-Calculus
A.Verify the identity. B.Determine if the identity is true for the given value of x. Explain. Sec(x) / tan(x) = tan(x) / [tan(x) – cos(x)],x = π I already solved A and I believe it's true; however, I need help with B.

calculus
Beast Mode Question: I am seating in one of the corners of the room when the time was exactly 12:30PM. I was decided to go to the other corner of the room at 12:35. I go outside of the room when the sun was directly ahead of me. Find the inclination of the sun at 2:00PM with ...

Calculus
Sketch a rough graph of the yield of a crop as a function of the amount of fertilizer used. I do not know what to do, can someone guide me?

Calculus II
If f(x) - x cos (x), how many intervals would be needed to approximate with the Trapezoidal Rule with an error of E<.01?

Calculus
find the intervals on which f is increasing and decreasing f(x)=(x-2)/(X^2-x+1)^2 I found the derivative a got a whole mess of things: ((x^2-x+1)^2-2(x^2-x+1)(2x-1)(x-2))/(x^2​-x+1)^4 Do I have to use the quadratic formula to solve for the vertices to find where it is ...

calculus 1
Find equations of all tangent lines to the graph y=4x3−19x+40 which pass through the point (2,2) ​(not on the​ curve).

Calculus
Give an example of a function with a critical point that is neither a maximum nor a minimum. Specify the relevant point(s). This is what I have and this is what I got wrong... A function with a critical point that is neither a maximum nor a minimum would be f(x)=x^2 if F(x) = ...

calculus
Find the dimensions of the rectangle of maximum area A that can be inscribed in the portion of the parabola y^2=4px intercepted by the line x=a. heres another problem pls help Damon!!! Graph it if possible

calculus
Match club charges annual membership dues of 100 pesos per member, less 0.50 cantavo for each member over 600 and plus 0.50 centavo for each member less than 600. How many members should give the club most revenue from annual dues? I'm spamming this question, need quick answer...

calculus
Match club charges annual membership dues of 100 pesos per member, less 0.50 cantavo for each member over 600 and plus 0.50 centavo for each member less than 600. How many members should give the club most revenue from annual dues?

maths sir-reiny help calculus
solve the differential equation (x^2-xy+y^2)dy-xydx=0 plz show me working

Calculus
Hello! I need help with this problem, its been irritating me for days! Any help would be greatly appreciated! Here’s the question.. The minute hand on a watch is 8 mm long and the hour hand is 4 mm long. How fast is the distance between the tip of the hands changing at 10:00...

calculus help
y=cosxcosy-sinxsiny/sinxcosy+cosxsiny find dy/dx plz show me working

Calculus
What type of discontinuity is this? f(x) = 2x+8,x<4 and x^2,x>4 I think it's a point discontinuity.

Pre-Calculus
This question has me stuck. Use the Pythagorean identity sin^2 Θ + cos^2 Θ = 1 to derive the other Pythagorean identities, 1 + tan^2 Θ = sec^2 Θ and 1 + cot^2 Θ = csc^2 Θ. Discuss how to remember these identities and other fundamental identities.

Pre-Calculus
tan theta = 1/2, what's sec theta?

Pre-Calculus
csc theta = sqr root of 5, what is cot theta?

Calculus
Write the equations of the circle in general form. 1. Points on circle (0,0), (0,8), (6,0) 2. Points on circle (1, -1), (2, -2), (0,-2). I don't know how to solve this given the fact that I don't know what the center or the radius of the circle is.

pre-calculus
sine theta = 1/3 and cos theta = 2/3, find tan theta

pre-calculus
sin theta = 1/4, find sin (-theta)

Pre-Calculus
csc theta = (sqr root 5) over 15, find sine theta

Math (calculus 3)
A football is thrown down the field by a quarterback from a height of 1 foot with an initial velocity of 40 feet per second at angle of pi/6 radians. If a receiver catches the ball downfield at a height of 1 foot above ground; a) How long was the ball in the air? b) What was ...

AP Calculus
A particle is moving along a horizontal straight line. The graph of the position function (the distance to the right of a fixed point as a function of time) is shown below. Answer the following questions only on the interval (0,8). 1. When is the particle moving toward the ...

Calculus
Thank you - (Enter your answers using interval notation. If an answer does not exist, enter DNE.) y = 4x + [5/sin x], (−π, π) concave upward (x,y)- concave downward (x,y)-

calculus help me
help find dy/dx if y=cot(x+y) working plz

Calculus
1. Use a graph to estimate the limit. Use radians unless degrees are indicated by θ°. (Round your answer to four decimal places.) lim θ → 0 θ/tan(7θ) 2. Assuming that limits as x → ∞ have the properties for limits as x → c, use ...

Pre-Calculus
If csc theta = square root of 5 divided by 15, find sin theta

Calculus
Find an equation of the tangent line to the graph of f at the given point. f(x) = x + (4/x), (4,5) I tried using the limit process a lot, but it didn't quite work. If possible, please use the limit process. Thanks a lot to whoever answers this question.

Pre-Calculus
Find two exact values of theta in degrees (0 less than or equal to theta < 360°) if cos theta = -(square root of 2)/2.

Pre-Calculus
Use a calculator to approximate two values of theta (0 <= theta < 2pi) if csc theta = 1.03. Round answer to two decimal places.

Pre-Calculus
Use a calculator to approximate two values of theta (0 <= theta < 2pi) if csc theta = 1.03. Round answer to two decimal places.

calculus help plllllz
if you go with the right substitution ∫[{(1-sin(x))/(1+sin(x))}{(2-sin(x​))/(2+sin(x))}] dx plz show me solution

calculus help me pllllllllllz
Find out what kind of improper integral is given below §dx/{x^4+4}....?,hence evaluate the integral with upper boundary=infinity lower boundary =0 i need help plz show me full work

Calculus
Water is flowing into a hemispherical bowl having a radius of 10cm at constant rate of 3cm^3/min. When the water is x cm deep, The water level rises at a rate of 0.0149 cm/min. What is the value of x?

Calculus
Construct a function f : R 2 ¡æ R such that its saddle points are given by {(n, 2m+1−n)|n ¡ô Z, m ¡ô Z}, where Z is the set of integers.

calculus
plz help show me steps solution evaluate the integral §dx/[(x+1)root(1-x^2)]

Calculus
Evaluate the limit using algebraic techniques. limit of (x^2 - 25)/(x^2 - 4x - 5) as x approaches 0. How do I do this?

Calculus
Find the set of points that the following function is continuous at them . f(x)= { (2x+1)/(x+3) if x<0 (√(x+4)-2)/2x^2-3xx if x>0 -1/3 if x=0

Calculus
Find all the values of a and b in such a way that f is continuous function on its domain. f(x)= { (√x+a)+1 if -a ≤x ≤ 0 2x^2+3 if 0 ≤ x ≤ 1 (x+b)^2+1 if x>1

calculus help
if y^3=6xy-x^3-1 show that the maximum value of y occurs where x^3=8+2sqrt(14)

Calculus
Even after looking up how to do this and reading about it I still don't know how to find the slope of curve or the deritives . Please help solve these problems. 1. Y =x^3 p(-1, -1) 2. Y = x^4 /2 p(-1 , 1/2) 3. Y= 8x^4 -7x^2 +5x + 6 p(-1,2)

Calculus
Suppose you know f′(a) = R, a, R > 0. If f is an odd function, what is f(−a)? Explain

calculus
a ladder 10m long is leaning against a vertical wall with its other end on the ground. the top end of the ladder is sliding down the wall , when the top end is 6m from the ground it is sliding down at 2m/sec. how fast is the bottom moving away from the wall at this instant?

Calculus
(kx^2)+m, x<-2 g(x)=e^(ln(2x+3))-2<x<3 kx-m, x>3 Find values of k and m

calculus need help
solve d^2y/dx^2+y=tanx plz help me aldo i was given a link to read on but i cant even acess it just help

maths calculus need help plz
solve d^2y/dx^2+y=tanx show working plz i don't no it at all

Calculus
Find a value for k so that the function is continuous. f(x) = {(x^2 + 2x - 15)/(x - 3), x ≠ 3 and 2kx - 4, x = 3 Is k = 2?

calculus help me asap
if y^6=tanh^-1(tan^-4(4x^2+y^2)^2)^9 find dy/dx show work....

Calculus 2
A culture of bacteria is growing at the rate of 20e^0.8t cells per day, where t is the number of days since the culture was started. Suppose that the culture began with 50 cells. (a) Find a formula for the total number of cells in the culture after t days. (b) If the culture ...

Calculus III
Topic: Quadric surfaces. I have two homework problems, and they are quite a doozy for me. So the point is, I am given details of a quadric surface on the Cartesian coordinate system, and thus have to use the data to construct an equation through it. ====================== Find...

calculus and chemistry
A container of hot liquid is placed in a freezer that is kept at a constant temperature of 10°F. The initial temperature of the liquid is 160°F. After 5 minutes, the liquid's temperature is 60°F. How much longer will it take for its temperature to decrease to 20°F? (Round ...

calculus
A container of hot liquid is placed in a freezer that is kept at a constant temperature of 10°F. The initial temperature of the liquid is 160°F. After 5 minutes, the liquid's temperature is 60°F. How much longer will it take for its temperature to decrease to 20°F? (Round ...

calculus plz help me
Show that the numerical value of the radius of curvature at the point (x1, y1) on the parabola y^2=4ax is [2(a+x1)^3/2)]/a^1/2. If c is the centre of the curvature at the origin O and S is the point (a, 0), show that OC=2(OS) plz show me working plz

calculus need help
If 3ay^2=x(x-a)^2 with a>0, prove that the radius of curvature at the point (3a, 2a) is 50a/3. Help with working plz

Calculus
If a ≠ 0, then the limit of (x^2 - a^2)/(x^4 - a^4) as x approaches a is: How do I do this type of problem?

Calculus AB
Please help I'm stuck on this problem for the past hour. Define f(x)= { Ln lx-1l }/x A) show that f(c) is continuous at x=2 B)Where on the interval [-2,2] is f discontinuous? Show the work that leads to your conclusion. C) classify the discontinuities in part b) as removable ...

stats
Jason, a freshman at a local college, just completed 15 credit hours. His grade report is presented below. Course: Calculus, Biology, English, Music, P.E. Credit Hours 5, 4, 3, 2, 1 Grades C, A, D, B, A The local university uses a 4 point grading system, i.e., A = 4, B = 3, C...

Calculus
Hello I need help with this excersise of derivative of a inverse function. The excersise says: If f(x+2)=x^3+1 and g(x)=f(arctg x), find the derivative of the inverse function of g(x) and then calculate (g^-1 (9))'[the derivative of the inverse function evaluated in 9] . I don...

Pre-Calculus 11
Two positive numbers x and 1-x add up to 1. Let the sum of their reciprocals be k. Find the only possible value of k such that x is a rational number. Hint: set up the equation and solve x with k in it. You'll encounter the quadratic formula in your solution.

Pre-Calculus/Math
a slow growing population of animals increases with time (years). the size of the population is given by P(t)=100+0.6t^2-0.004t^3. how fast is the population changing after 10 years?

Calculus integrals
Suppose f(x)=∫ (from 0 to x) (t^2-36)/2+cos^2(t) dt. For what value(s) of x does f(x) have a local maximum?

Calculus
Hello all, I would like some confirmation on a limits question. The limit is as h --> 0, [sqrt [73-5(x+h)] - sqrt (73-5x)]/h I multiplied by the conjugate of the numerator and reduced everything down to this final answer: [(-5)sqrt(73-5x)]/2 Is this correct?

differential calculus
A bulldozer costs \$120,000 and each year it depreciates 8% of its original value. Find a formula(equation) for the value V of the bulldozer after t years.

Calculus
Find the velocity and position vectors of a particle that has the given acceleration and the given initial velocity and position. a(t) = 2 i + 6t j + 12t2 k, v(0) = i, r(0) = 2 j − 7 k

Calculus
Find the tangential and normal components of the acceleration vector. r(t) = t i + t2 j + 4t k aT= aN=