Lesson Example Discussion Quiz: Class Homework |
Quiz At Home |
Title: Calculus |
Grade: Top-SAT3 Lesson: S6-P2 |
Explanation: Hello Students, time to practice and review. Let us take next 10-15 minutes to solve the ten problems using the Quiz Sheet. Then submit the quiz to get the score. This is a good exercise to check your understanding of the concepts. |
Quiz: at Home
| Problem Id | Problem | Options |
|---|---|---|
1 |
Find the derivative of \$v(x) = (x cos(x))/(x^2 - 1)\$. |
A) \$(x^3 sin(x) - x^2 2cos(x) + x sin(x) - cos(x))/(x^2 + 1)^2\$ B) \$(-x^3 sin(x) - x^2 cos(x) + x sin(x) - cos(x))/(x^2 - 1)^2\$ C) \$(-x^3 sin(x) - x^2 cos(x) + x sin(x) - 3cos(x))/(x^2 - 1)^2\$ D) \$(x^3 sin(x) + x^2 cos(x) + x sin(x) - cos(x))/(x^2 + 1)^2\$ |
2 |
Evaluate the integral: \$ \int tan^3x sec^5x dx \$. |
A) \$ (1/2) sec^7x - (1/5) sec^5x + C \$ B) \$ (1/7) sec^7x - (1/8) sec^5x + C \$ C) \$ (1/7) sec^5x - (1/5) sec^3x + C \$ D) \$ (1/7) sec^7x - (1/5) sec^5x + C \$ |
3 |
Write the fifth term in the sequence defined by \$a_1 = 1,000\$; \$a_n = 1.005a_n-1 + 1,000 (n > 2)\$. |
A) 5044.065 B) 5034.065 C) 5024.065 D) 5134.065 |
4 |
Consider the infinite series \$ \sum_{n=1}^\infty (n^3)/(2^n) \$. Determine whether this series converges or diverges; find its sum if it converges. |
A) Diverges B) Not converges C) Converges D) None of these above |
5 |
Convert each number to polar form. \$ 4sqrt(2)- 4i sqrt(2) \$. |
A) \$ 6( cos(pi/2) + i sin (pi/5)) \$ B) \$ 8( cos(-pi/4)+i sin (-pi/4)) \$ C) \$ 6( cos(pi/2) - i sin (pi/5)) \$ D) \$ 2( cos(pi/2) - i sin (pi/5)) \$ |
6 |
Find the derivative of the function \$p(x) = (xsin^2(4x))/(\sqrt(x^4 - 2))\$. |
A) \$((sin2(4x) + 8xsin(4x)cos(4x)) \sqrt(x^4 + 2) - (xsin^2(4x)) ((2x^3)/\sqrt(x^4 - 2)))/(x^4 + 2)\$ B) \$((sin2(4x) + 7xsin(4x)cos(4x)) \sqrt(x^4 - 2) + (xsin^2(4x)) ((2x^3)/\sqrt(x^4 - 2)))/(x^4 - 2)\$ C) \$((sin2(4x) + 8xsin(4x)cos(4x)) \sqrt(x^4 - 2) - (xsin^2(4x)) ((2x^3)/\sqrt(x^4 - 2)))/(x^4 - 2)\$ D) \$((sin2(4x) + 8xsin(4x)cos(3x)) \sqrt(x^4 - 2) + (xsin^2(4x)) ((2x^3)/\sqrt(x^4 - 3)))/(x^4 - 2)\$ |
7 |
\$ \int (x^2 - 2)/(x^3 - 6x + 1) dx \$. |
A) \$ (1/6) ln|x^3 − 6x + 1| + C \$ B) \$ (1/3) |x^3 − 4x + 1| + C \$ C) \$ (1/2) ln|x^3 − 6x + 1| + C \$ D) \$ (1/3) ln|x^3 − 6x + 1| + C \$ |
8 |
Determine the value of \$ ∑_(n = 101 to 1000) 3n + 2 \$. |
A) 1, 411, 150 B) 1, 228, 150 C) 1, 488, 150 D) 1,233,150 |
9 |
Find the quotient \$ z1/z2 \$ if \$ z1 = 12 cis (2pi/3) \$ and \$ z2 = 10 cis(3pi/4) \$. |
A) \$ (3/5) cis(-pi/12) \$ B) \$ (6/5) cis(-pi/8) \$ C) \$ (6/5) cis(-pi/12) \$ D) \$ (1/5) cis(-pi/12) \$ |
10 |
Given that z = 1 + i, find \$z^2024\$. |
A) \$ 2^(1012)\$ B) \$ 2^(1210)\$ C) \$ 3^(1210)\$ D) \$ 3^(1012)\$ |
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