Question

Calculus 1 MAT 201 Final Exam, Spring 1 2019, LAGCC Evaluate the following limits, you may use L'Hospital's rule, if it applies. -V31+4 lim 4-1 -4 a. b. Evaluate the following limit. lim xIn x x-0 2. Evaluate and explain your answer -xsin(x)+cos (x) x+1 130 dx (a.) 130 Differentiate each of the following below using the fundamental theorem of calc part 1 X cos? (1- 51) dt ) g (x) = S_ e (2c) g(t)= J x2t+1 3 Use Newton's Method to find the root of X -5x9x +3 = 0 accurate to 2 de in the interval 4. Use implicit differentiation to find y' for each of the following

Answer 1

1)

a)

(t-sqrt(3t+4))/(4-t)

So, at t=4, limit tends to 0/0

So, apply L'hospital rule

So,

it can be written as

-(1-3/sqrt(3t+4))

So, at t=4

Limit is -(1-3/4)=-1/4

b)

x*log(x)=log(x)/(1/x)

So, at x=0, limit is inf/inf

So,apply L'hospital rule

So,

(1/x)/(-1/x^2)=-x=0

So, LIMIT=0

2)

A)

Integral is 0 since the upper limit and lower limit of integral both are 0

b)

Apply lebnitz rule

So, g'(x)=exp(2x)*cos(1-5x)^2

c)

Apply lebnitz rule

So, it is

(-(x^8+1)/(x^4+1))*(2*x)