Calculus Answers

3. If y= cos^ −1 x, then d/dx (y) is
4. If y = arctan x, then x is
5 If y = arc sin x, then x^ 2 is
6 If y = arcsin x, then dx/dy is

The differential coefficient of y = sin(3x+2) is
lim x→−3 (x 3 +5) =

6. A function y = f(x) is said to be differentiable at point x = a if ……..

A. it possesses a differential coefficient and differentiable at a point x = a

B. it does not possesses a differential coefficient but differentiable at a point x = a.
C. it possesses a differential coefficient and not differentiable at a point x = a.

D. it possesses a differential coefficient and differentiable at any point x

3 One of the following is not true

A. Every rational function is continuous everywhere except at the points where the denominator vanishes.
B. The function y =1/x have an infinite discontinuity at x = 0.

C. The function y =cos1/x is undefined at x = 0.

D. The function y = cos1/x is defined and possesses a limit at x = 0.

4. One of the following is false

A. Every polynomial of any degree is continuous for all x.

B, Every polynomial of any degree is discontinuous for all x.

C. Every rational function is continuous everywhere except at the points where the denominator vanishes
D. The function y = 1/x have an infinite discontinuity at x = 0.

lim x→1 (1+x+x2 +……...+x m−1 ) =

Determine if the series converge absolutely, converge conditionally, or diverge. If it is absolutely convergent, find its sum.
a) ∑ (3/(n(n+1)) + 2^-n), n=1 to infinity
b) ∑ (cos(nπ)·arctan(n)), n=1 to infinity

Please find the definite integration of the following function
f(t) = e^-(a*t+((b^2)/(4*t)))/(t^(3/2))

from 0 to t (with respect to t).

what is integrals??? is it an operator or no??

Find a vector that has direction angles α = 75° and β = 128°.

Fully explain your method. Is there more than one possible answer?

Why?

What do they have in common?

Scientists are studying the temperature on a distant planet. They find that the surface temperature at one location is
50°
Celsius. They also find that the temperature decreases by
7°
Celsius for each kilometer you go up from the surface.
Let
T
represent the temperature (in Celsius), and let
H
be the height above the surface (in kilometers). Write an equation relating
T
to
H
, and then graph your equation using the axes below.