25,270 Answered Questions for the topic calculus

Calculus

08/11/23

please help with this

At noon, ship A is 20 nautical miles due west of ship B. Ship A is sailing west at 18 knots and ship B is sailing north at 24 knots. How fast (in knots) is the distance between the ships changing... more
Calculus

08/11/23

please help with this

Gravel is being dumped from a conveyor belt at a rate of 40 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is... more
Calculus

08/11/23

Please help me to solve this problem!

Use Newton's method to find the absolute maximum value of the functionf(x) = 5x cos(x),    0 ≤ x ≤ 𝜋,correct to six decimal places.please help me to solve this problem. I've got the wrong answer.
Calculus

08/11/23

Since I don't have graphing calculator.. how to find the answer of this?

A graphing calculator is recommended.Use Newton's method to find all solutions of the equation correct to eight decimal places. Start by looking at a graph to find initial approximations. (Enter... more
Calculus

08/11/23

Newton Method, please help me

Consider the following -2x^5+9x^4− 7x3 − 14x = 0,    [3, 4]Use Newton's method to approximate the solution correct to six decimal places.I know how to solve the problem with the Newton method, but... more
Calculus

08/10/23

Please Help with this

When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are related by the equation PV^1.4=C where C is a constant. Suppose that at a certain instant the volume... more
Calculus

08/10/23

im not sure how to do this

The altitude of a triangle is increasing at a rate of 1.5 centimeters/minute while the area of the triangle is increasing at a rate of 1 square centimeters/minute. At what rate is the base of the... more
Calculus Precalculus

08/10/23

Please help me ASAP

It's about sketching the graph based on precalculus and calculus. draw the graph y=(1+e^x)^-2 When I tried to first derivative test, I couldn't see at any point that makes 'f'(x)=0' Does it right?... more
Calculus

08/10/23

Velocity Function of a Particle

The velocity function of a particle moving along a line is v(t)=t^2-7t +10, where t is in seconds and v is in m/s. Find the distance traveled by the particle during the time interval [-1,7]
Calculus Precalculus

08/10/23

Please help me. How I should change ln(t) to "e to the something"?

This problem is about parametric function and I have to eliminate parametric function. x=lnt y=root t I can see that y=e^x/2How does the x=lnt change to "e to the something"?
Calculus Math

08/09/23

How do I solve this integration by parts question with tan-1?

Using integration of parts, find the exact value of ∫tan-1(1/2x) dx between the limits of 2 and 0.After I apply the integration by parts rules, I obtain tan-1(x) •x-ln(x2+4) between 2 and 0 however... more
Calculus

08/08/23

Why here we don't use l'hopital rule?

lim (root x/(1+e^x))x-> infinity The answer of this problem is 0 and I can't understand why we don't use l'hopital rule in here. (because, I think root x goes infinity and... more
Calculus

08/08/23

About first derivative test (ID test)

Q. Find the intervals on which f is increasing and decreasing. f(x)= (x^2-24)/(x-5)-> The answer is that f is increasing in (negative infinity, 4), (6, positive infinity) and decreasing in (4,... more
Calculus

08/08/23

A man launches A man launches his boat from point A on a bank of a straight river, 3 km wide, and wants to reach point B, 1 km downstream on the opposite bank...

Q. A man launches his boat from point A on a bank of a straight river, 3 km wide, and wants to reach point B, 1 km downstream on the opposite bank, as quickly as possible (see the figure below).... more
Calculus

08/08/23

Suppose a package to be mailed using a certain postal service may not measure more than 138 inches in length plus girth.

Suppose a package to be mailed using a certain postal service may not measure more than 138 inches in length plus girth. (Length is the longest dimension and girth is the largest distance around... more
Calculus

08/08/23

Find the arclength of the curve with x=3t-1, y=4t+9 with 2<t<6

Calculus

08/07/23

This is confusing me

Please explain HOW so I know what to doIf a ball is thrown straight up with an initial velocity of 70ft/sec. Its height after t seconds is given by y=70t-16t^2. Find the average velocity for the... more
Calculus

08/03/23

Calculate length

Calculate the length of the following parameterized curve over the given interval. r(theta) = <sin(theta) - theta cos(theta), cos(theta) + theta sin(theta)> , 0 <= theta <= 5
Calculus

08/03/23

The position vector of an object

The position vector of an object r(t) = < t^2/2 cos sqrt(2t)i + t^2/ sqrt(2) sin sqrt(2t)j + 22-tk. Calculate the time t takes for the object to reach z = 0. Then compute the distance L traveled... more
Calculus

08/03/23

Use newton method to approxumate the solution cos x= x^2-4 to six decimal places

How I should find solve this problem?Also, I want to know what the graph looks like.
Calculus

08/03/23

Verify rolles theorem and find all values of c

Verify that rolle's theorem can be applied to the function f(x)=x^3-8x^2+17x-10 on the interval [1,5]. Then find all values of c in the interval such that f '(c)=0.
Calculus

08/02/23

Suppose the position equation for a moving object is given by

Suppose the position equation for a moving object is given by s(t)=6t2-5t+4 where S is measured in meters and T is measured in seconds. a) find the average velocity on the interval [1, 4] b) Find... more
Calculus

08/02/23

Use the definition of derivative to find F ' (x) given that

Use the definition of derivative to find F ' (x) given that F(x)=2x2-5x+3 (do NOT use the short cut method). Use the result to find the slope of the tangent line at the point (-1, 10).

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