# Calculus midterm review questions

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```					Determine if y = 4x2 – x has symmetry
to the x-axis, y-axis, or origin.

Determine if y = 5x5 – x has symmetry
to the x-axis, y-axis, or origin.

Determine if y = -4x2 + x has
symmetry to the x-axis, y-axis, or
origin.

Write the equation of a graph that has
intercepts x =  2 and is symmetric
with respect to the y-axis.

Given f(x) = 4 – x2 and g(x) = 5x + 2,
find f(g(x)).

Sketch the graph of f(x) = 3 sin x.
Sketch the graph of f(x) = 4 cos x.

t 4
lim t 2  16

t 4

2 x 4
lim      x

x 0

x 4
2

lim 3 x 4  8
x 

Use the graph of f(x) to evaluate each
limit.

Find the slope of the tangent line to
3     2
the graph of f(x) = x – 5x at the point
where x=2.
Find the derivative of the following
function using the limit process:

g(x) = 8x -8

Find the derivative of the following
function using the limit process:

y = 3x2 – 4

Find the slope of the graph f(x) = 2 +
2
x when x = 8.
Find an equation for the tangent line to
the graph of f(x) = x  1 at the point
where x = 3.

Sketch the graph of y = 5x + 1 and its
derivative y’.

2
Sketch the graph of f(x) = x and its
derivative, f’(x).

Give the intervals where the following
functions are differentiable.
h(x) = x + 5
Give the intervals where the following
functions are differentiable.
g(x) = |x – 3|

Determine if f(x) is differentiable
always, sometimes, or never.

 2 x  2, x  0
 2              
f(x) =  x  2, x  0 

Determine if f(x) is differentiable
always, sometimes, or never.

3 x  1, x  2
 2            
f(x) =  x  1, x  2

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