Question 16:

Use differentials to estimate the maximum error when measuring the volume of the sphere if the possible error in measuring the radius is 0.5 in. (Hint: The formula for the 4 volume of a sphere is V0) = E TU3.) O 65,144.07 m3 0 452.30 m3 0 32,572.03 m3 o 16,266.02 m3 \fLet f(x) = (12x2+36)5. Find the differential, of. O of = 5(12x2 + 36)4 O of = 5(12x2 + 36) Adx O df = 120x(12x2 + 36)4 O of = 120x(12x2+ 36)4dxWrite Newton's formula used to approximate a solution of the equation 2x -x - 15 =0 and find the third iteration value. Be sure to verify both parts of the answer are correct when making your selection. 2xn'-Xn - 15 O Xn+ 1= Xn- ; X3 ~ 2.042527942 2-1 6Xn 2xn - Xn-15 O X n+ 1 = 2+ ; X3 ~ 1.857593743 6x2- 1 2xn'-Xn-15 O X n+ 1 = 2 - 6x2- 1 -; X3 ~ 2.044471717 2xn'-Xn-15 O Xn+ 1 = Xn- ; X3 ~ 1.872499451 6x- - 1\fUsing logarithmic differentiation, find the derivative of y = (cosx) 3x. O dy = (cosx)3*(3In(cosx) + 3xtanx) dx O dy = (cosx) 3*(3In(cosx) -3xtanx) dx O ay = 3In(cosx) - 3xtanx dx O dy = 3In(cosx) + 3xtanx dxFind the derivative of f(x) = 3x sinx + 8cosx. O f(x)= 15x*sinx - 3x-cosx + 8sinx O f'(x) = 15x *sinx + 3x-cosx -8sinx O f(x) =15x*sinxcosx - 8sinx O f'(x)= - 15x*sinxcosx + 8sinxFind the derivative of y = arctan(5x2 - 1). dy 10x O = dx 25x4 - 10x2+2 dy 10x O dx 25x4 - 10x2 + 2 dy O dx 25x4 - 10x2+ 2 dy O dx 25x* - 10x-+ 2Use the limit definition of the derivative to find f'(x) when f(x) = 7x2. O f(x) = 14x Of ( x) = 0 Of( x) = 2x O f(x) = 14x+7hWrite an equation of a line tangent to the graph 3X2 = - 31/2 + 75 at the point (-4. - 3). Find the derivative of f(x) = - 15sinx + X -+37x-5. O f(x) = - 15cosx + 11 CO 4x 3 + - 5 7v O f(x) = 15cosx + 11 3 4x 3 7y O f(x) = - 15cosx - 44 3 5 + X 6 7 7y O f(x) = 15cosx 44 CO + 7y