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MTH 102 Practice Questions MTH 102 Objective Question
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Question

Evaluate Δy/Δx of the derivative of e^(3x+1) using first principle
Options
A (e^(3x+1)/3)[3+3Δx/2+(3Δx)²/3+(3Δx)³/4+...]
B (e^(3x+1)/3)[3+3Δx/2+(3Δx)²/3!+(3Δx)³/4!+...]
Correct Answer
C e^(3x+1)[3+3Δx/2+(3Δx)²/3!+(3Δx)³/4!+...]
D e^(3x+1)/3
Correct Answer

Option B is the correct answer.

Detailed Explanation

Δy/Δx = e^(3x+1)(e^(3Δx)-1)/Δx. Expanding e^(3Δx)-1 as a Maclaurin series and dividing by Δx (with a factor of 3 pulled out) gives (e^(3x+1)/3)[3+3Δx/2+(3Δx)²/3!+(3Δx)³/4!+...].

Hint

Expand e^(3Δx) as a Maclaurin series before dividing everything by Δx.

Question Info

Course: MTH 102
Topic: Practice Questions MTH 102
Type: Objective
Difficulty: Not specified
Question 927 of 930
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