Calculus Answers

Show that Sigma infinity n=1 ( -1)^n+1 5÷7n+2 is conditionally convergent

The volume of a cube is increasing at a rate of 1200 cm3/min at the

moment the lengths of the sides are 20 cm. How fast are the lengths of

the sides increasing at that moment?

1. Let f be the function deÖned by

f (x) = x^2/(-2x + 1)^2

(a) Determine the vertical and horizontal asymptotes (show all limits).

(b) Use the sign pattern for f'(x) to determine

(i) the interval(s) over which f rises and where it falls;

(ii) the local extrema.

(c) Use the sign pattern for f''(x) to determine

(i) where the graph of f is concave up and where it is concave down.

(ii) the inflection points (if any)

Locate and classify all critical points for f(x, y) = 4y^2x + 3xy

Check the limit of the function f(x,y) = 3x^2y/(x^2 + y^2) at origin exist or not

Waterisbeingpouredattherateof2⇡m3/min.intoaninvertedconicaltankthat is 12-meter deep with a radius of 6 meters at the top. If the water level is rising at the rate of 61 m/min and there is a leak at the bottom of the tank, how fast is the water leaking when the water is 6-meter deep?

Transform the general equation of circle : x2 + y2 + 4x - 2y -11 =0 to its standard form or center-radius form. After transforming , identify the center and the radius then sketch the graph in the Cartesian coordinate plane .

Determine if the following functions are continuous or discontinous at the given value of x.

1. f(x)= 3x+2x+1 at x= -2

2. f(x)= 9x2-1 at x=1

3. f(x)= 1/x-2 at x=2

4. f(x)= x-1/x^2 -1 at x=1

5. h(x)= x+1/x-1at x=1

6. f(x)= x^2 -2x+1 at x=3

7. f(x)= x/(x+2)(x-3) at x=2

8. f(x)= |x| at x=0

9. f(x) Cube root√x^2 -4 at x=5

10. f(x)= x+1/x-1 at x=0

A firm faces the demand function

P = 190 - 0.6Q and the total cost function

C = 40 + 30Q + 0.4Q2