Calculus

Find an equation of the normal line to the curve of y= square root of x that is parallel to the line 4x+y=1 y= -6x+57

Determine the interval of convergence of the series sumlimits _n=0 ∈ fty x/3 n. _ __ -3,3 _

Analyze and sketch a graph of the following function. Find any intercepts, relative extrema, points of inflection, and asymptotes. If an answer does not exist, enter DNE. y=frac x2+2x2-25 Determine the domain of the function. Enter your answer using interval notation. square Determine the range of the function. Enter your answer using interval notation. squa...

Given the function y=-3x2-4x4 , find dy/dx in any form. Answer Attempt 1 out of 2 dy/dx =6x-12x2sin x+3x2-4x3cos x S

Show that d/dx ln kx= d/dx ln x , given that x>0 and k>0 is a real number. Compute the derivative of the natural log of kx. Begin by letting u=kx , and substituting u into the equation. d/dx ln kx= d/dx In u square ° Compute the derivative using the chain rule. d/dx ln u=square d/dx u

Use the limit comparison test to determine whether sumlimits _n=11 ∈ fty a_n=sumlimits _n=11 ∈ fty frac 4n3-9n2+116+7n4 converges or diverges. a Choose a series sumlimits _n=11 ∈ fty b_n with terms of the form b_n=frac 1np and apply the limit comparison test. Write your answer as a fully simplified fraction. For n ≥ 11, limlimits _nto ∈ fty frac a_nb_n=limli...

We are now ready to find the rate at which the area of the rectangle is increasing when the length is 6 feet and the width is 3 feet. Gather the values you identified in Step 2 and Step 5 and substitute these values into the related rates equation, dA/dt = dL/dt W+ dW/dt L. How fast is the area of the rectangle increasing when the length is 6 feet and the wi...

spherical iron ball 10 in. in diameter is coated with a layer of ice The thickness of the ice is changing at a rate of uniform thickness. If the ice melts at a rate of 15in.3 /min, at in./min when the ice is 4 in. thick. hat rate is the thickness of the ice changing when it is 4 in. thick? Type an exact answer, using π as needed. what rate is the outer surfa...

bIs f'15 positive or negative? Is f'45 positive or negative? Explain. f'15 is square because fis square there. f'45 is square because fis square there eTextbook and Media c Find f30 and f'30 analytically. Interpret them in terms of the concentration of the drug in the body. Round f30 to the nearest integer and f'30 to one decimal place. f30= i square mg/ml f...

Problem 4. Determine whether the function fx is continuous at x=2. fx= beginarrayl 6/x 02endarray .