SaiBook.us SAT-3

Lesson Example Discussion Quiz: Class Homework

Quiz In Class

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: in Class

Problem Id	Problem	Options
1	\$ \int ((18x - 17)/((2x - 3)(x + 1))) dx \$ =	A) \$ 2 ln\|2x − 3\| + 7 ln\|x + 1\| + C \$ B) \$ 7 ln\|2x − 3\| + 2 ln\|x + 1\| + C \$ C) \$ 8 ln\|2x − 3\| + 7 ln\|x + 1\| + C \$ D) \$ 4 ln\|2x − 3\| + 7 ln\|x + 1\| + C \$
2	For the equation \$ sin(xy) + e^xy = x^2 + y^2 \$, find \$ dy/dx \$.	A) \$ (4x − y(cos(xy) + e^xy))/(x(cos(xy) + e^xy) − 4y) \$ B) \$ (4x − y(cos(xy) + e^xy))/(x(cos(xy) + e^xy) − 2y) \$ C) \$ (2x − y(cos(xy) + e^xy))/(2x(cos(xy) + e^xy) − 2y) \$ D) \$ (2x - ycos(xy) - e^(xy)y)/(xcos(xy) + e^(xy)x - 2y) \$
3	Find the derivative of \$ y = ((sin(x))^cos(x))/2 \$.	A) \$ (1/4)sin^(cos(x))(x) (sin(x) ln(sin(x)) + 2cot(x)cos(x)) \$ B) \$ (1/2)sin^(cos(x))(x) (-sin(x) ln(sin(x)) + 2cot(x)cos(x)) \$ C) \$ ((sin(x))^cos(x)/(cos(x))^sin(x)) (cos^2(x) cot(x) + sin^3(x) tan(x)) \$ D) \$ ((sin(x))^cos(x)/(cos(x))^sin(x)) (cos^4(x) cot(x) + sin^4(x) tan(x)) \$
4	Find the sum of the first 250 terms of the sequence defined by \$a_n = 12n - 7\$.	A) 357, 750 B) 300, 050 C) 374, 750 D) 344, 350
5	Evaluate the definite integral: \$ \int_0^2 (3x^2 + 2x + 1)dx\$	A) 12 B) 18 C) 16 D) 14
6	For the equation \$ x^3 + y^3 = 6xy \$, find \$ dy/dx \$.	A) \$ (3y − x^2)/(y^2 − 2x) \$ B) \$ (4y − x^2)/(y^2 − 2x) \$ C) \$ (2y − x^2)/(y^2 − 2x) \$ D) \$ (y − x^2)/(y^2 − x) \$
7	Convert \$ 10cis(pi/3) \$ to rectangular form.	A) \$ 5 + (5i(\sqrt 3)) \$ B) \$ 5 - (5i(\sqrt 3)) \$ C) \$ 5 + (3i(\sqrt 6)) \$ D) \$ 2 + (2i(\sqrt 3)) \$
8	Find the product of \$ z_1 = 12 cis((2pi)/3) \$ and \$ z_2 = 10 cis((3pi)/4) \$	A) \$ 120 cis((11pi)/12) \$ B) \$ 120 cis((17pi)/12) \$ C) \$ 110 cis((17pi)/12) \$ D) \$ 150 cis((15pi)/12) \$
9	Solve the integral: \$ \int (sin^5x/cos^3x) dx \$.	A) \$ (1/2)sec^4x + 2 ln\|cosx \| - (1/2)cos^4x + C \$ B) \$ (1/2)sec^2x + 4 ln\|cosx \| - (1/2)cos^2x + C \$ C) \$ (1/2)sec^2x + 2 ln\|cosx \| - (1/2)cos^2x + C \$ D) \$ (1/4)sec^2x + 2 ln\|cosx \| - (1/2)cos^2x + C \$
10	A ball is dropped from a height of 10 meters and bounces back 70% of the previous height on each bounce. What is the total distance the ball travels forever (infinite bounces) using an infinite geometric series?	A) 33.33 meters B) 16.67 meters C) 23.67 meters D) 46.12 meters

Problem Id

Problem

Options

\$ \int ((18x - 17)/((2x - 3)(x + 1))) dx \$ =

A) \$ 2 ln|2x − 3| + 7 ln|x + 1| + C \$

B) \$ 7 ln|2x − 3| + 2 ln|x + 1| + C \$

C) \$ 8 ln|2x − 3| + 7 ln|x + 1| + C \$

D) \$ 4 ln|2x − 3| + 7 ln|x + 1| + C \$

For the equation \$ sin(xy) + e^xy = x^2 + y^2 \$, find \$ dy/dx \$.

A) \$ (4x − y(cos(xy) + e^xy))/(x(cos(xy) + e^xy) − 4y) \$

B) \$ (4x − y(cos(xy) + e^xy))/(x(cos(xy) + e^xy) − 2y) \$

C) \$ (2x − y(cos(xy) + e^xy))/(2x(cos(xy) + e^xy) − 2y) \$

D) \$ (2x - ycos(xy) - e^(xy)y)/(xcos(xy) + e^(xy)x - 2y) \$

Find the derivative of \$ y = ((sin(x))^cos(x))/2 \$.

A) \$ (1/4)sin^(cos(x))(x) (sin(x) ln(sin(x)) + 2cot(x)cos(x)) \$

B) \$ (1/2)sin^(cos(x))(x) (-sin(x) ln(sin(x)) + 2cot(x)cos(x)) \$

C) \$ ((sin(x))^cos(x)/(cos(x))^sin(x)) (cos^2(x) cot(x) + sin^3(x) tan(x)) \$

D) \$ ((sin(x))^cos(x)/(cos(x))^sin(x)) (cos^4(x) cot(x) + sin^4(x) tan(x)) \$

Find the sum of the first 250 terms of the sequence defined by \$a_n = 12n - 7\$.

A) 357, 750

B) 300, 050

C) 374, 750

D) 344, 350

Evaluate the definite integral:
\$ \int_0^2 (3x^2 + 2x + 1)dx\$

A) 12

B) 18

C) 16

D) 14

For the equation \$ x^3 + y^3 = 6xy \$, find \$ dy/dx \$.

A) \$ (3y − x^2)/(y^2 − 2x) \$

B) \$ (4y − x^2)/(y^2 − 2x) \$

C) \$ (2y − x^2)/(y^2 − 2x) \$

D) \$ (y − x^2)/(y^2 − x) \$

Convert \$ 10cis(pi/3) \$ to rectangular form.

A) \$ 5 + (5i(\sqrt 3)) \$

B) \$ 5 - (5i(\sqrt 3)) \$

C) \$ 5 + (3i(\sqrt 6)) \$

D) \$ 2 + (2i(\sqrt 3)) \$

Find the product of \$ z_1 = 12 cis((2pi)/3) \$ and \$ z_2 = 10 cis((3pi)/4) \$

A) \$ 120 cis((11pi)/12) \$

B) \$ 120 cis((17pi)/12) \$

C) \$ 110 cis((17pi)/12) \$

D) \$ 150 cis((15pi)/12) \$

Solve the integral: \$ \int (sin^5x/cos^3x) dx \$.

A) \$ (1/2)sec^4x + 2 ln|cosx | - (1/2)cos^4x + C \$

B) \$ (1/2)sec^2x + 4 ln|cosx | - (1/2)cos^2x + C \$

C) \$ (1/2)sec^2x + 2 ln|cosx | - (1/2)cos^2x + C \$

D) \$ (1/4)sec^2x + 2 ln|cosx | - (1/2)cos^2x + C \$

A ball is dropped from a height of 10 meters and bounces back 70% of the previous height on each bounce. What is the total distance the ball travels forever (infinite bounces) using an infinite geometric series?

A) 33.33 meters

B) 16.67 meters

C) 23.67 meters

D) 46.12 meters