Calculus Answers

Given that the graph of y=f(x) is symmetric about the y-axis and the gradient of the curve at any point (x, y) is 2x+b. Find the value of b.

Consider the function f and its graph given to the right.

Find ​a) lim

x→−3−

 g(x)​; ​b) lim

x→−3+

 g(x)​; ​c)lim

x→−3

 g(x).

If a limit does not​ exist, state that fact.

use the fundamental theorem of integral calculus to evaluate the integral integration of 0 to 1 ( 2xsinx 1/x - cos.1/x )dx

Using weiestrass M test show that the following series converges uniformly sigma infinity n=1 n³ x^n x€[-1/3,1/3]

A tank can be filled by a pipe in 18 hours. Five hours after this pipe is opened, it is supplemented by a smaller pipe, which, by itself can fill the tank in 22 hours. Simultaneously, a drainpipe is opened, which, by itself, can completely empty the tank in 30 hours. Find the total time, measured from the opening of the larger pipe, to completely fill the tank.

why did (7-a)^2 + (2-b)^2 = R^2 become (2-b)^2 - b^2= 0

Find the inverse function of 𝑓(𝑥) = −𝑥² + 8𝑥 − 14 if 𝑥 ≤ 4. Find the domain of this inverse function.

A remittance company charges its customers based on the delivery rate table as shown. Amount is in Philippine peso.

Destination 1kg (max) 3kg (max) 5kg (max) 10kg (max) 20kg (max)

NCR 120 160 220 420 820

Luzon 150 190 320 620 1220

Mindanao 150 190 370 720 1420

(a) Write a rule of a piecewise-defined function C such that C(x) is the charge due on a weight x kg for NCR.

(b) Graph the function in (a)

(c) Use the table to find C (12.3) in Mindanao

(d) Use the table to find C(2.2) in Luzon

Find the domain and range and sketch the graph of the function f(x)= sqrt 16+6x-x²