provide me with a step-bystep work on each-and-every offered problem with verbal explanation.

1. Find the following limits:

lim

xV5+x2

x2 3x+2+x

lim eu+5,

and

x2-36

lim

X-6 (x-6)(x+4)

.

u>-5

2. Determine values of x for which the following functions are continuous

f(x)

x2-11x+7

,

X+3

g(x) = x – 3Vx, and h(x) = In(x2 – 1).

5

=

w

.

3. Use the definition of the derivative to find f'(x) and g'(w) for the functions

f(x) = 2x – x2 and g(w) –

4. Upon using the Basic Rules of Differentiation, find the derivatives of the functions

f(x) = 5×3 – 2×2 + x – 7

and

g(x) = 2 + x* – 21.

5. Find an equation of the tangent line to the graph of

f(x) = 4×6 – x +1 at (0.1).