Basic Rules of Diferentiation Questions Response

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).