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[answered] Math 114, Worksheet #9 Question 1:( 10 points) Find the val


I need help with all of them if possible. ?Thanks. ?The exercises are on the pdf


Math 114, Worksheet #9

 

Question 1:( 10 points) Find the value of the following limit:

 

lim n?? n

 

X ?

 

i

 

( n + ? )?2

 

n

 

i=1 1 Question 2: (a) ( 10 points) Find y?. Do not simplify.

 

y= Z R sin x

 

1 1 1

 

dt

 

1+t2 1

 

dt

 

1 + t2 (b)

 

(10 points) Let f beZ a differentiable function that satisfies

 

Z

 

x 2 5 f (t)dt = cos(2x) + 1 x (cos t)f (t)dt, find f 0 ( ?2 ). 2 Question 3: Compute the following integrals:

 

(a) (10 points) Z 3 ||x ? 6| ? 7|dx ?2 (b) (10 points) Z 3

 

?3 e2 + x3 ln(1 + x2 )

 

dx

 

x4 + 2 3

 


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