Exam 1: The Derivative

Find the slope of the line with equation 3y + 2 = 5x - 2y?

If g(t) = - $3 \mathrm { t } ^ { 2 }$ + 2t - 3, find $\frac { g ( a + h ) - g ( a ) } { h }$ and simplify. Enter your answer exactly as a polynomial in a in standard form.

Use limits to compute f'(1) where f(x) = $\frac { 1 } { 2 - 5 x }$ . Enter just a fraction in lowest terms or an integer.

For the following function g(x), determine whether or not $lim _ { x \rightarrow 2 }$ g(x) exists. If so, give the limit.

Let y = $\sqrt { 5 t ^ { 2 } - 6 }$ . Compute $\frac { \mathrm { dy } } { \mathrm { dt } }$ $\mathrm { t } = 2$ . Enter just a reduced fraction of form $\frac { a } { b }$ .

Write the word or phrase that best completes each statement or answers the question. -y = 3 $\sqrt { 5 x ^ { 2 } + 2 }$ Enter your answer exactly as: $\frac { d y } { d x } = \frac { P ( x ) } { \sqrt { Q ( x ) } }$ where P(x) and Q(x) are polynomials in standard form.

Write the word or phrase that best completes each statement or answers the question. -y = $\sqrt { 3 x ^ { 2 } + 4 x }$ Enter your answer exactly as: $\frac { d y } { d x } = \frac { P ( x ) } { \sqrt { Q ( x ) } }$ where P(x) and Q(x) are polynomials in standard form.

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Calculate the following limit(s) if they exist. - $\lim _ { x \rightarrow \infty }$ $\frac { 2 x ^ { 2 } + 1 } { x ^ { 2 } + 1 }$