Calculus Answers

The acceleration of a particle at any time is given by a = 12e

3t

i − 8sin2tj +

4tk. If the velocity is zero at t = 0, find velocity.

Trace the curve , x^2= y^2((x+1)^3 ) stating all the properties used in the process.

Integrate (1/(x+1)) dx within the limits 0 to 4 in four parts using Simpson rule

Consider the curve y=f(x) of the function

f(x)=e^(2x-x^2)

A)Find the domain of f

B)Find the x,y-intercept

C)Find f'(x) and f''(x)

D)Find the critical points of the function f

E)Find where the curve is increasing and where its decreasing

F)find the point of inflection if any and discuss the concavity of the curve

G) identify any asymptotes

I)plot the key points and sketch the curve

At which point on the following curve does the tangent line has the largest slope ?

y=1+40x^3-3x^5

Find dy/dx by implicit differentiation

tan(x-y)=y/1+x^2

0 "\\int" 2 (x-x^3)dx represents the area under the curve y=x-x^3 from 0 to 2.

Explain and give an example of why this statement is false. Also, refer to integral properties in your answer.

Is the following statement true or false. Give an explanation and an example of your answer.

if f' is continuous on [1, 3], then the integral which goes from 1 to 3 "f' (v) d(v) = f(3) - f(1)" ?

Let F be the R²-R function defined by f(x,y)=Inxy and let r be the R-R² function defined by r(t)=(e^t;t).

1.determine the composite function F o r: (simplify your answer).

2.determine gradf (x,y) and r'(t).

3.determine the derivative function (f o r)' by

3.1.differentiating the expression obtained in (1).

3.2.using the chain rule (theorem ) compare your answer.