1. Find the limit. lim (sqrt(x+1)-2)/(x-3) x->3 2.Find the limit. lim f(x + delt

Question

1. Find the limit.

lim     (sqrt(x+1)-2)/(x-3)

x->3

2.Find the limit.

lim   f(x + delta x)-f(x)/delta x

x->0

f(x)=(x^2)-4x

3.Find the limit(if it exists). If it doesn't exist, explain why.

lim  |x| / x

x->0 from the left

4.Find the x values(if any) at which f is not continous. Which of these discontinuties are removable?

f(x)= cos ((pi*x)/2)

5.Determine wheher f(x) approaches infinity or negative infinity as x approaches 4 from the left and from the right.

f(x)= 1/(x-4)

6.Find the vertical asymptotes (if any) of the graph of the function.

a) f(x)=1/(x^2)

b) f(x)= tan(pi * x)

7.find the one-sided limit(if it exists).

lim  1/ (x+1)

x->-1 from the right

MUST SHOW WORK

Explanation / Answer

5) first one is -infinity

in this case x is almost 4 and approaches from the left ( this means from the left of the number) , for example 3.99999999

and 1/(x-4)= 1/(3.9999999-4) = 1/ -(0.000001) .= - 100000000.
the closer x gets to 4, the number will be 'more' negative ( ie. -infinity)

second one is infinity

in this case x is almost 4 an approaches 4 from the right, for example 4.00000000001
and 1/(4.00000001-4) = 1/0.00000001 = 100000000
the closer x gets to 4, the number will be greater ( ie. infinity)

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