Calculus Answers

Write a polynomial function of minimum degree in standard form with real coefficients whose zeros and their multiplicities include those listed.
2 ​(multiplicity 2), 7+i​ (multiplicity 1)

Find the limit of the function by using direct substitution.

limit as x approaches zero of quantity x squared minus one.

solve: d^2/dx^2 - 2 tan x dy/dx + 5y = e^x sec x

Solve : d^2y/dx^2 -2tanx dy/dx +5y = e^x. sec x

Find by using polar coordinated in R^2 the volume of the region bounded by the paraboloid z= 16-x^2-y^2 and the xy-plane ( having equation z=0)

if y=tan¯¹ x, obtain an equation showing the relationship between y n+2, y n+1 and y n

An efficiency study of the workers at a factory shows that an average worker who comes to work at 8:00am will have produced Q(t) =-t³+9t²+12t units t hours later. At what time during the morning is the worker performing most efficiently.

Q. What are the projections of helix (acost, asint, t) in all three coordinate planes xy-plane, yz-plane, xz-plane.

implicit differentiation
Find dy/dx for:
a) e^cosx + e^siny = 1/4
b) e^2x+3y = x^2 -ln(xy3)

x − y + 2 = 0 is a tangent to the curve 3 2 (x + y) = (x − y + 2) at (−1, 1) is it true or false.justify the answer