Calculus

Rationalize the numerator of the following expression:

• 10-3(10)^1/2

• 10+3(10)^1/2

• 10/3(10)^1/2

• 3(10)^1/2+2

What is the conjugate of a^1/2 -b^1/2

• −a^1/2−b^1/2

• b^1/2−a^1/2

• −a^1/2+b^1/2

• a^1/2+b^1/2

The slope of the tangent is said to be the ........................ of the slope of the secant as Q approaches P along the curve.

What does it mean if lim⁡ x→c f(x)=∞?

• The function is continuous at x=c

• The function has a horizontal asymptote at x=c

• The function grows without bound in the positive direction as x approaches c.

• The function has a zero at x=c

if does not change its ....................... at c, then is ........................ a local minimum or a local maximum.

• sign, both

• sign , neither

• interval, neither

• symbol, neither

Differentiate p(x)=5e^x+7e^(−x)

• 5e^x+7e^x

• 5e^x−7e^x

• 5e^x−7e^−x

• -5e^x−7e^−x

Use the second derivative to

• determine the domain and any discontinuities

• determine where the graph is concave up and where it is concave down

• find any points of inflection

• determine the intercepts

When sketching the graph of a polynomial or rational function we use the function to

• local maximum and minimum points

• find any asymptotes, and determine function behaviour relative to these asymptotes

• determine the intercepts

• determine the domain and any discontinuities

We can use the first derivative to;

• find the critical numbers

• determine where the function is increasing and where it is decreasing

• identify any local maxima or minima

• determine the domain and range

Differentiate the following;

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