Exam 1 (derivatives,slope,limits)

Question 1

Techniques for finding limits

Answer 1

Factoring, rationalize/conjugate, get a common denominator

Question 2

Horizontal asymptotes

Answer 2

Is when limit as X approaches infinity or negative infinity is equal to a number. At that number there is a horizontal asymptote.

Question 3

How to prove horizontal asymptote limits

Answer 3

Divide highest power of variable from the denominator to all terms

Question 4

A function is continuous if/when

Answer 4

1.f(a) is defined
2.limf(X) exists
X-a
3.limf(X) =f(a)

Question 5

For square roots they are only continuous for

Answer 5

All odd roots

for even roots—-f(a)>0

Question 6

Instantaneous rate of change

Answer 6

Velocity at a specific moment

Slope of Tangent line

Question 7

Slope of tan line=

Answer 7

Lim f(X+h) - f(X) / h 
h-0

Question 8

A function is not differentiate at a point when

Answer 8

1. not continuous
2. sharp corner
3. when the graph is vertical

Question 9

Derivative of e^kx

Answer 9

ke^kx

Question 10

Derivative of cos(X)

Derivative of sin(X)

Answer 10

-sinx

Cosx

Question 11

Slope of secant line/ average velocity

Answer 11

Y2-y1/x2-x1