Mat 175 Midterm Examination Review Fall 2018 PDF

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Midterm Practice...

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Mat 175 Midterm Examination Review NAME:___________________

Fall 2018

1. Find the following limits: [21 pts] x 2  9 x  20 (a) lim x 5 x 2  25

(c) lim x 0

(b) limx  

4x 2  10x  6 3x 2  5x  6

7  9 x  7  5x 3x

2. Find dy / dx : [32 pts] (a)

5  sin( x) y 10  cos(x )

(c)

y ( x 2  1) 50 e

x

(b) y ln(x 2  e 3 x ) (d)

y  6  4 sin( x)

[Problems 3 – 7: 10 pts each [ 50 ] 3. Let f ( x) 2  3 x 2 and compute f '( x) from the definition as a limit.

x

3 4. Find the equation of the line tangent to y 4 sin( x )  5 cos(x )  6e at the point (0, 11)

5. A object is thrown upwards at a speed of 32 ft/sec from a platform of height 32 ft. What is the velocity of the object on impact with the ground ?

6. A 23 ft. ladder is leaning against a wall and the top is sliding down the wall at 3 ft/sec. How fast is the foot of the ladder moving away from the wall when it’s 16 ft from the base of the wall.?

7 Find the equation of the line tangent to the curve 5 x 2  xy  y 2 11 at the point (1, 2) ....