367 Answered Questions for the topic Calculus 2

Calculus 2


Volume of solid by rotating it

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.y = x2, x = y2; about y = 1

Points of discountity

how do we find the points of discountity of f(x)=8x/5x^2-1?   If i made the denominator =0 i would get squared 1/5 and then when i will plug it back it will be undefined or am i doing it wrong !   more


Confused about limits?

As lim x approaches -3 of x^2-3x/x^2-9   1.how can you solve it in a step by step i am really confused 2. When finding the sided limit we subsitutw in the original function or after we factor it?
Calculus 2 Calculus Domain Integral


How can you compute the domain of g and g'(t) without computing any integrals in its definiton?

g(t)= ∫0t((1/1-x)+(1/(1+x)^2))dx  


Consider the differential equation dy/dx=x^2+4y-1. If y=f(x) is the solution to the differential equation, at what point does f have a relative maximum?

Possible answers include:   A. (3, -2) B. (0, 1/4) C. (-2, -1) D. (-5,-6)

calculus question, need help please!

Let R be the region in R^2 enclosed by the curve y = x^2 + 3 and the line y = 4x + 3.   a)  Write the area of R as a definite integral.   b)  Calculate the area of R.
Calculus 2


find the derivative of (sech(4x))^2

I calculated the answer to be -8sech^2(4x)tanh(4x) but i'm not sure if it is correct. 


Tempuratures using Trig Function

Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies between 38 and 52 degrees during the day and the average daily temperature first... more
Calculus 2


Use known Taylor Series to find the value for...

Use known Taylor Series to find the value for:  (π is Pi character) π/3 - π/3^3 * 3!  + π/3^5 * 5!  - π/3^7 * 7! + ......
Calculus 2


Suppose f(x) is a function with continous Derivatives...

Suppose f(x) is a function with continous Derivatives and.. f(8) = 4   f'(8)= 5   f''(8)=-4   f'''(8)= 1   a.) Write the Taylor Polynomial of degree 3 (first four terms) of f(x) centered at... more
Calculus 2 Calculus Integrals


How do I solve this Integral? (Pic attached in link)

I have been stuck on this integral for 3 hours. Here is what I have so far.. : https://ibb.co/mWAC7x
Calculus 2


How to prove that the limit lim_{(x,y)->(1,2)} (e^{y(x-1)}-1)/(1-x)(y+1) exists and equal to -2/3 ?

Prove that   


Which limits do you use when finding arclength of a rose?

What is the arclength of r=6sin(3θ)? Given the formula Lpolar= ∫√[r^2+(dr/dθ)^2]dθ I can find the arc length using the r stated above and r'=18cos(3θ) Given that one petal is between θ of 0 and... more


how do I simplify these trig expressions?

cos-1(cos(47pi/12) arcsin(tan(-pi/6)) csc-1(cos(2017pi/2018)) cot(arcsin(1/2 csc(-11pi/4)))
Calculus 2


What Double Integral represents and its applications?

I want Correct answer
Calculus 2 Math Math Help Integrals


This was on my first Calc 2 quiz: $2\int_{-3}^{3}e^x^4dx$

I feel that there should be another x in the problem so that u sub works, or something, as it is I believe it is a partial gamma function or something, but I know we should not learn those until... more
Calculus 2 Fractions Integration


Fractions Equal??

Just wondering: Are these two quantities equal?(2/3)x^3 = 2x^(3)/3 ??Please be as detailed in your explanation as possible, perhaps proving your response. It is appreciated!
Calculus 2 Math Calculus Math Help


Consider the function f(x)=e^(3x)*g(x) , where g(0)=13 and g′(0)=−2 Find f′(0)

 This is for my homework I need an explanation of how to do this. please
Calculus 2


What is the formula for the sequence -3,5,-7,9,-11...

Find a formula for sn for n>1, for the sequence -3, 5, -7, 9, -11 ...
Calculus 2


Calculus II Magnitude and Direction of Vectors

I have worked this problem at least 8 different times and keep getting the same answer every single time. Could somebody please explain how to work this problem? Here is the problem: The magnitude... more
Calculus 2 Math Calculus Math Help


I'm having trouble with series.

Let f(x)= ∑∞n=0 (x^n)/(n!) Find f(0)= 1 f(1)= e f'(x)= f(x) f''(x)= f(x) Not exactly sure how we're supposed to go about finding those answers, or how to start.
Calculus 2


Sequence and bounds

I found that the limit of the sequence (1+22/n)^n is e^22. I'm told the sequence is bounded because the absolute value of an is < or = to e^22 for all positive integers.    I would like to... more
Calculus 2 Physics


How much a force will stretch a spring

Suppose that a spring has a natural length of 20 cm, and that 7 J of work is needed to stretch from a length of 30 cm to 50 cm. How far beyond its natural length will a force of 28 N keep the... more

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