Calculus Answers

The displacement of a mass is given by the function y=sin3t

The displacement of a mass is given by the function y=sin3t

a) draw a graph of the displacement y(m) against time t (s) for the time t= 0s to t=2.s?

b) identify for the position of any turning points and whether they are maxima, minima or points of inflexion?

c) calculate the turning points of the function using differential calculus and show which are maxima, minima or points of inflexion by using the second derivative?

d) compare the results from part b and c?

Let f and g be functions on R^n defined by f(x) = e^(-|x|^2), xER^n, and g(x) = 1, xER^n. Compute (f*g)(x) for all xER^n.

Ascertain that (del)(r^n)=nr^n-2 vector r

Evaluate the following integral if D is the region bounded by xy=a, xy=b, xy^1.4=c and xy^1.4=d, where 0< a < b and 0< c < d. ∫ ∫ D x^8y^10 dA. Note: D should be at the bottom of the second integral, it is not part of the function.

Show that

∫ₐᵇ (ln x)/(x) dx = (1/2) ln ab ln(a/b)

Does N satisfy the Archimedean property? justify your answer.

Find all the asymptotes of the curve,

x³+y³ = 3axy, where a>0.

please solve it very urgent

check whether every integrable function is differentiable or not ? justify

The graph of the function y = x+|x| for all x belongs to Q is strictly increasing or not ?

Evaluate
∫√(1+√x) dx