Calculus Answers

Tell whether if the following piecewise function is a continuous at a given point or not. (SHOW THE SOLUTION).

3. at x = 5

x² - 3 if x ≥ 5

4x + 2 if x < 5

Tell whether if the following piecewise function is a continuous at a given point or not. (SHOW THE SOLUTION).

1. at x = 4

x + 1 if x < 4

(x - 4)² + 3 if x ≥ 4

Tell whether if the following piecewise function is a continuous at a given point or not. (SHOW THE SOLUTION).

1. at x = 4

x + 1 if x < 4

(x - 4)² + 3 if x ≥ 4

2. at x = 0

1/x if x ≤ -1

x² - 2 if x > -1

3. at x = 5

x² - 3 if x ≥ 5

4x + 2 if x < 5

CONTINUITY AT A POINT

A. Tell weather if the following is a continuous or discontinuous at a given point.

1. f(x) = 3x² + 2x + 1 at x = -2

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

3. f(x) = x-1/x² -1 at x = 1

4. f(x) = log (x² - 3) at x = 2

5. f(x) = 9x² - 1 at x = 1

Check whether the sequence (an), where

an = 1/ (n+1) + 1/(n+2) +....+1/(2n) is convergent or not

State if the following statement is true or false. Give reasons for your answers in the form of a short proof or a counterexample.

(√2, 1, ½) E Q X Z X R.

State is the following statement is true or false. Give reasons for your answers in the form of a short proof or a counterexample.

The domain of the function f defined by f(x)= √(3-x)/(x-2) is R-{2}.

) The function g is related to one of the parent functions g(x) = −(x − 2)^3 a.) Identify the parent function f. b.) Use function notation to write g in terms of f.

You are working as a Junior Engineer for a small motor racing team. You have been given a proposed mathematical model to calculate the velocity of a car accelerating from rest in a straight line. The equation is: 𝑣(𝑡) = 𝐴 (1 − 𝑒 − 𝑡 𝑡𝑚𝑎𝑥𝑠𝑝𝑒𝑒𝑑)

Ascari A10 5.0 V8 - [2006] t=2.8 tm(400)= 10.36 tmaxspeed= 7.8

derive an equation a(t) for the instantaneous position of the car as a function of time? Identify the acceleration of the car at t = 0s and asymptote of this function as t → ∞?

The region in the first quadrant, which is bounded by the curve

x² = 4y, the line x = 4, is revolved about the line x = 4. Locate the

centroid of the resulting solid of revolution.