Calculus Answers

Find the maxima and minima, if any, for the function f given by
f(x)= x^4-14x^2+24x+6
Also find the values of the function at those points.

The point P(21, 28) is on the terminal side of θ. Evaluate sin θ.

Show that the functions f(x,y)=In x-In y and g(x,y)= x2+2y2/2xy are functionally dependent.

Find the domain and range of the function f defined by f(x,y)=3x2y2/(x2+y4)

If f(x,y)={x sin(1/y)+ysin(1/x), xy not=0
{0, xy=0
Then Show that the repeated limits of f do not exist. Examine the function f for simultaneous limit at the origin.

Give an example, with justification, of a periodic function which is not even.

Verify f, defined by f(x)=x^3+4x+1 on [1,5] satisfies Lagrange's mean value theorem

Prove that
In=[sec^(n-2) xtanx]/n-1 + (n-2)/(n-1) ×In-2
Where In = Integration of sec^n dx Hence deduce I4

Differentiate cos^-1 (2x^2- 1)
with respect to sin^-1 √(1-x^2)

Calculate the approximate value of
Integration of x^3 dx within limit 0 to 6
by taking 6 subintervals of equal length
and applying Simpson’s rule.