Calculus

Find the equation of the tangent line in slope-intercept form to the graph y=4x2ln 5x-9 when x=2. Note: no need to simplify derivative since you are finding it purely to plug in an x —value

What is the derivative of frac 6x4 ? 6ln x4 6x-4 frac 14x3 -24x-5 -24x-3 24x3

Find the limit, if it exists. If an answer does not exist, enter DNE. limlimits _xto -5frac x2-25x+5 × You may not have checked if the function can be simplified first.

Express the integrand as a sum of partial fractions and evaluate the integrals. ∈ t frac x+82x3-18xdx Rewrite the integrand as the sum of partial fractions. frac x+82x3-18x=square Evaluate the integrals. ∈ t frac x+82x3-18xdx=square Use parentheses to clearly denote the argument of each function.

fx Predict which statements are true about the intervals of the continuous function. Check all that apply. -3 -15 over the interval - ∈ fty ∝ ° underline 3. fx>0 -2 0 fx ≤ 0 over the interval [0,2]. fx<0 over the interval -1,1. -1 3 fx>0 over the interval -2,0. 0 0 over the interval [2,_ ∈ fty . fx ≥ 0 1 -3 2 0 3 15

Once/Kale's kite reaches a height of 55 it above her hands, it rises no higher but drifts due east in a wind blowing 7 ft/s. How fast is the string running through Kate's hands at the moment that she has reessed 103 it of string? Lela be the horizonal distance from Kate to the kite and z be the length of the string. Write an equation relating x and z

Differentiate the function. rz=z-4-z1/2 r ° z=square

Find the derivative of the following function. y=93x4 Answer y'=square

Oetermine whether the integral is convergent or divergent. If it is convergent, evaluate it ∈ t _-23frac 39x4dx

Suppose w and v are functions of x that are differentiable at x=2 and that u2=-2 u'2=4 v2=-3 v'2=-1.