Calculus Answers

The tangent to the curve 𝑦 = 2𝑥²− 5𝑥 + 6 at the point (2,4) intersects the normal to the same curve at the point (1,3) at point 𝑄. Find the coordinates of 𝑄

Consider the function, f(x)=2x³ - 24x² -7. Find the intervals of x where f(x) is

increasing or decreasing.

Find the coordinates of the points on the curve 𝑦 = 3𝑥³ − 2𝑥² − 12𝑥 + 2 where

the normal is parallel to the line 𝑦 =− 𝑥 + 1.

the tangent to the curve 𝑦 = 𝑥² − 5𝑥 − 2 at the point (1,-6) intersects the normal to

the same curve at the point (2, -8) at point P . find the coordinates of P

Apply definition of antiderivative and find area under the curve of f(x) = x^1/2 between x=0 and

x=1

Find absolute maximum and minimum of the function f(x) = 2x^2- 5 in [-1, 2].

6. Determine whether each of the following statements about Fibonacci numbers is true or false. Note

The first 10 terms of the Fibonacci sequence are 1, 1, 2, 3, 5, 8, 13, 21, 34, and 55.

a. If n is even, then F is an odd number.

b. 2F-Fn-2 = Fn+1 for n 23

Determine whether if lim f(c) = f(c)

x→c

1. f(x) = x+2; c = -1

2. f(x) = x-2; c = 0

3. (at c = -1 )

f(x) = {x ² - 1 if x < -1}

f(x) = { (x - 1) ² - 4 if x ≥ -1}

4. (at c = 1 )

f(x) = {x³ - 1 if x < 1}

f(x) = { x² + 4 if x ≥ 1}

Activity in Limit Theorems

Compute the following limits.

1. lim (4 • f(x))

x→c

2. lim (g(x) - h (x))

x→c ________

3. lim √12 • f(x)

x→c

4. lim (g(x) + h(x)) / f(x)

x→c

5. lim (f(x) + h(x))

x→c

Activity in Limit Theorems

Directions: Assume the following.

lim f(x) = 3/4;

x→c

lim g(x) = 12;

x→c

lim h(x) = -3;

x→c