1.) intergral of (x^5)(e^(x^3)) dx 2.) intergral of (2x^2-9x+2)/ (x(3x-1)^2) dx

ID: 2845410 • Letter: 1

Question

1.) intergral of (x^5)(e^(x^3)) dx

2.) intergral of (2x^2-9x+2)/ (x(3x-1)^2) dx

3.) Applying an appropriate trig substitution, the following integral can be transformed as

the integral from 5sqrt3/9 to 5/3 of x(sqrt 9x^2+25) dx = the integral from a to b of f(theta) d(theta)

In the above transformation f(theta)=___________________, a=___________,b=____________

4.) Evaluate the limits

a) lim x-sinx/x^3+x^2

x->0

b) lim (1 + 2/x)^x

x->infiniti

5.) Determine which of the functions grow faster or show that they both grow at the same rate.

a) x^3 + sqrt x and ln(x) + 3x^3

b) 2^3x and e^x

1.(x^3-1)e^(x^3)

3. function = 25/3.tan(theta).sec(theta)

a= pi/6, b= pi/4

(a)0

(b)e^2

(a)lnx + 3x^3 grows faster

(b)2^3x grows faster

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