6,212 Answered Questions for the topic calculus


Help please - integral evaluation

Please evaluate the integral: Options: x4 + 2x3 - x + C


Calculus help needed please

Which of the following statements is/are true? I. If f '(x) > 0 on (a, b), then f(x) is increasing on [a, b].II. If f(a) = f(b), then there exists a number c in (a, b) such that f '(c) = 0.III.... more


Help with Calculus

The side length of a rectangular box with a square base is increasing at the rate of 2 ft/sec, while the height is decreasing at the rate of 2 ft/sec. At what rate is the volume of the box changing... more


Help with Calculus question

Given the relationship x2 + 3y2 =12, with y > 0 and  = 2 units/min., find the value of  at the instant y = 1 unit. Question options: 1)  units/min 2)   units/min 3)  -2 units/min 4)  0... more


Interval of moving object

Given the position function,  , between t = 0 and t = 9, where s is given in feet and t is measured in seconds, find the interval in seconds where the particle is moving to the right.Question... more


Finding velocity and acceleration

Given the position function s(t), s(t) = t3 - 5t, where s is measured in meters and t is in seconds, find the velocity and acceleration of the particle at t = 3 seconds.Question options: 1) 12... more


Function zero problem

find all rational zeros of this functionf(x) = 3x4 + 16x3 - 59x2 - 400x - 400


Rational Zeros of Function

find all the rational zeros of these functionsx3 - 10x2 + 23x - 14x3 + 6x2 + 9x + 4


Find polynomial function with real coefficients that has the given zeros

4, -5i 4, 7 + i


Find all zeros of the functions

What are all the zeros of these two functions?x(x-3)2(x-3)(x+9)3


Minima or Maxima

Approximate (to two decimal places) any relative minima or maxima f(x) = 3x2 - 2x - 5 f(x) = x3 - 3x2 - x + 1 f(x) = x(x-2)(x+3)


Which of the following relations are functions

Which of the following relations are functions 1. y= -x + 22. x= -y + 23. x - y = 2Answer choicesA. All of themB. Choice 1 onlyC. Choice 2 onlyD. Choice 3 only


Pair of functions that satisfies the limit

For which pair of functions f(x) and g(x) below will the  ?Question options: 1) f(x) = ex; g(x) = x3 2)  f(x) = x5; g(x) = ex 3)  f(x) = x3; g(x) = ln(x) 4)  f(x) = x-2; g(x) = e-x more


Need help with the mean value theorem

If f(x) = |(x2 - 6)(x2 + 2)|, how many numbers in the interval 1 ≤ x ≤ 2 satisfy the conclusion of the mean value theorem?Question options: 1) None 2)  One 3)  Two 4)  Three


Stuck on this calculus problem please help

A 15-ft ladder rests against a vertical wall. If the top of the ladder slides down the wall at a rate of 0.33 ft/sec, how fast, in ft/sec, is the bottom of the ladder sliding away from the wall, at... more


Please help me with this calculus problem

The height of a cylinder with a fixed radius of 4 cm is increasing at the rate of 2 cm/min. Find the rate of change of the volume of the cylinder (with respect to time) when the height is... more


propogated error in cm^2 and relative error

The radius of a circular disk is measured as  30cm with a maximum error in measurement of +/- 4 cm. Use differentials to estimate the propagated error and the relative error in the calculated area... more


Finally, when the top of the ladder is 6 ft above the ground, the rate at which the bottom of the ladder is sliding away from the wall is

 A 18-ft ladder is leaning against a wall, and the top of the ladder is sliding down the wall at a constant rate of 1.75 ft/s. How fast is the bottom of the ladder sliding away from the wall when... more


A cylindrical can without a top must be constructed to contain V=2100cm3 of liquid. Find the base radius r and height h that will minimize the amount of material needed to construct the can.

I am just completely lost on this question. I am a first year student trying to take calc one online and I am completely struggling.


Vector and parametric equation

1) What is the vector and parametric equation for: the horizontal line through (pi,e)2) At time t, the position of an object moving with constant velocity is given by the parametric equations... more


factoring polynomial

using the factors (3x + 2) & (x - 1), find the remaining factor(s) of f(x) = -6x4 + 23x3 - 12x2 - 11x + 6 and write polynomial in fully factored form.


Calculus 2 sequence of natural numbers expressions

a(n)=2n2 +1 for n belonging to natural numbers N. Compute the following expressions 1) a n*42) a* (n • a* a * 3)3) a*(a * a * i) *means subI’m so lost. I thought maybe it was asking for a sequence... more


Projectile Motion using Vector Calculus

Trebuchet can throw an 80 lb rock up to 100 yards. The maximum height that the rock reaches as it flies through the air toward a fortress wall 100 yards away is 20 yards, calculate the initial... more


Write the definite integral for the summation



The domain for f(x) and g(x) is the set of all real numbers. Let f(x) = 2x2 + x − 3 and g(x) = x − 1. Find f(x) • g(x).

The domain for f(x) and g(x) is the set of all real numbers.Let f(x) = 2x2 + x − 3 and g(x) = x − 1.Find f(x) • g(x).
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