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NDA 2020
Exam
NDA
Year
2020
Subject
Mathematics
Chapter
Limits

NDA 2020 · Mathematics · Limits

What is _ x arrow 1 (x+x^2+x^3-3)/(x-1) equal to ?

What is lim⁡x→1x+x2+x3−3x−1\lim _{x \rightarrow 1} \frac{x+x^2+x^3-3}{x-1} equal to ?

Options

  1. A1
  2. B2
  3. C3
  4. D6

Correct answer

D. 6

Step-by-step solution

lim⁡x→1x+x2+x3−3x−1\lim _{x \rightarrow 1} \frac{x+x^2+x^3-3}{x-1} This is in 00\frac{0}{0} form, so we can use L' Hospital rule. lim⁡x→1x+x2+x3−3x−1=lim⁡x→11+2x+3x21=1+2+31=6\lim _{x \rightarrow 1} \frac{x+x^2+x^3-3}{x-1}=\lim _{x \rightarrow 1} \frac{1+2 x+3 x^2}{1}=\frac{1+2+3}{1}=6
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