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Calculus Exam for College Students

The document is a preliminary exam for a differential calculus course. It contains 10 sections with multiple questions in each section. The sections cover topics such as evaluating functions, finding domains and ranges, composing functions, computing derivatives, finding inverses of functions, and evaluating limits. The exam tests students' understanding of key concepts in differential calculus.

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91 views1 page

Calculus Exam for College Students

The document is a preliminary exam for a differential calculus course. It contains 10 sections with multiple questions in each section. The sections cover topics such as evaluating functions, finding domains and ranges, composing functions, computing derivatives, finding inverses of functions, and evaluating limits. The exam tests students' understanding of key concepts in differential calculus.

Uploaded by

IamJmlingcon
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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CALAMBA DOCTORS’ COLLEGE

Km. 49 National Highway, Brgy. Parian, Calamba City


Laguna, Philippines 4027

DIFFERENTIAL CALCULUS
Prelim Examination

I. Given f(x) = -x2 + 6x – 11, find each of the following:


1. f(2) 4. f(t-3)
2. f(-10) 5. f(x+5)
3. f(t) 6. f(4x – 1)
II. Find the domain and the range of the following functions:
1. f(x)= 6x – 1 4. g(x) = 8
𝑥−4
2. f(x) = √4 − 7𝑥 5. f(x) = 2
2 𝑥 −2𝑥−15
3. f(x) = -2x + 12x + 5
III. Given f(x) = 3x2 – x + 10 and g(x) = 1 – 20x, find each of the following
1. ( f ○ g ) (5) 4. ( g ○ g ) (x)
2. ( f ○ g ) (x) 5. ( f ○ f ) (-3)
3. ( g ○ f ) (x)
1 2
IV. Given f(x) = 3x – 2 and g(x) = 3 𝑥 + 3 find each of the following:
1. ( f ○ g ) (x) 2. ( g ○ f ) (x)
𝑓(𝑥+ℎ)− 𝑓(𝑥)
V. Compute ℎ
, h ≠ 0, if
2
1. f(x) = x -1
2. f(x) = x2 + 2
VI. Find the inverse of y = f(x).
1. y = 4x + 1 1
5. 𝑦 = 𝑥
2. y = -7x + 5 4
𝑥 𝑦 6. 𝑦 = 2𝑥−1
3. + =4
2 3
4. 𝑦= x3 – 1 7. 𝑦 = √𝑥 − 4
VII. If f(x) = 2x – 7, find f(-2) and f-1(-2)
1
VIII. If h(x) = -x - 2, find h(-1) and h-1(-1)
IX. Evaluate the following:
𝑥 3 −1 𝑥 2 −81
1. lim 6. lim
𝑥→1 𝑥−1 𝑥→9 √𝑥−3

𝑥 2 −6𝑥 3− √5+𝑥
2. lim 𝑥 2 −7𝑥+6 7. lim
𝑥→6 𝑥→4 𝑥−4

√𝑡 𝑥 2 −𝑥−2
3. lim 8. lim
𝑡→1 𝑡 2 +𝑡−2 𝑥→−1 𝑥 2 +3𝑥+2

1 (1+𝑥)2 −1
4. lim 9. lim
𝑥→5 𝑥−5 𝑥→0 𝑥

𝑥 4 −16 𝑥−3
5. lim 10. lim
𝑥→2 𝑥−2 𝑥→3 √𝑥 2 −9

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