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Calculus (MAT-251) Graded Exam 1 2.1 2.2 2.3 3.1 3.2 4.1 4.2 Midterm 1 2 Final Exam 1 2

Lesson 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Calculus I (MAT-251)
Graded Exam 4a

Find the particular solution to = x if y(2) = 5

Answer: y = x² + 3

Explanation

What does arctan 0 equal?

Answer: 0

No explanation necessary.

What does arcsin (sin (5 TT/4)) equal?
Answer:
Explanation:

Evaluate the following as true or false.
Every function of the form f(x) = c – x is its own inverse, for and choice of c.

Answer: True

No explanation necessary

Which one of the following functions is invertible?

Answer:

No explanation neccessary

Solve the following differential equation for the general solution:

xy².
Answer: y =
Explanation

Evaluate:

Answer: 2 ln|x + 2| + 6ln|x – 2| + C

Explanation

What is the area of the region between the curves: y = x³ + x²- 1 and y = 2x² +2x – 1

                        Answer: 32/12

Explanation:
Eliminate like terms.
(y) = x³+ x²– 1 = 2x²+ 2x -1
Solve for x:       x = -1, 0, or 2   Substitute 0 for x = 2x²+ 2x − 1 =
y = 2(0)²+2(0) − 1 =     y=-1
Evaluate y when x = 2 = y = 2(2)²+ 2(2) − 1 =     y = 11
Evaluate y when x = −1 = y = 2(−1)²+ 2(−1) − 1 =              y = -1
The solution to the system is the complete set of ordered pairs that are valid solutions
(0, −1)    (2, 11)     (−1, −1)
∫^0,-¹x³ +x²-1- (2x² +2x-1) =     5/12 + ∫^2,02x² +2x-1- y-x³ +x²-1 =         8/3

5/12 + 8/3 = 37/12

Every function of the form f (x) = c − x is its own inverse, for and choice of c

Answer: True

No explanation necessary.

Evaluate

Answer: 5 ln|x + 3| + 5ln|x | + C

Explanation:

'

Evaluate

Answer: + x + 5ln|x - 1| + C

Explanation

What is the value of

[f^-1 (x)] when x = 0, given that f(x) = and f^-1(0) = 0?
Answer: 1

Explanation:
f(x) = x / 1 - x
y = x / 1 - x
x = y / 1 - y
f^-1(x) = x / x + 1
f^-1(0) = 0
d/dx[f^-1(x)] = d/dx [ x /1 + x] = 1 / (1 + x)²
d/dx[f^-1(0)] = 1 / 1 = 1

What is the value of :

Answer: 1

Explanation

Evaluate:

Answer: ln |x| + ln|x - 2| + C

Explanation

Evaluate:

Answer: ln |x| + ln |x - 7| + C

Explanation

What does arcsin

equal?
Answer:

Explanation

Solve    = 3 + y tan

            Answer: y = 3tan x + C sec x ü

Explanation

Calculus (MAT-251) Graded Exam 1 2.1 2.2 2.3 3.1 3.2 4.1 4.2 Midterm 1 2 Final Exam 1 2
Lesson 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Need Homework Help? Need A Tutor?

Evaluate: