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	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)) \$
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	\$ \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 \$
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	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) \$
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	Evaluate the definite integral: \$ \int_0^2 (3x^2 + 2x + 1)dx\$	A) 12 B) 18 C) 16 D) 14
8	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 \$
9	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) 23.67 meters B) 16.67 meters C) 33.33 meters D) 46.12 meters
10	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)) \$

Problem Id

Problem

Options

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)) \$

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) \$

\$ \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 \$

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

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) \$

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) \$

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

A) 12

B) 18

C) 16

D) 14

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) 23.67 meters

B) 16.67 meters

C) 33.33 meters

D) 46.12 meters

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)) \$