Mathematics

If $$f(x) =  \dfrac{2 \sin x- \sin2x}{x^3}$$ where $$x\neq 0$$, then $$\lim_\limits {x \to 0} f(x) $$ has the value; 


ANSWER

$$1$$


SOLUTION

$$\lim_{x \to 0}f(x)\\=\lim_{x \to 0}(\frac{2sinx-sin2x}{x^3})\\=\lim_{x \to 0}(\frac{2[x-(\frac{x^3}{3!})+(\frac{x^5}{5!})-....]-[(2x)-(\frac{2x^3}{3!})+(\frac{2x^5}{5!})+....]}{x^3})\\=\lim_{x \to 0}(\frac{x63((\frac{-1}{3})+(\frac{4}{3}))+x^5(....)+higher term}{x^3})\\=(\frac{-1}{3})+(\frac{4}{3})=(\frac{3}{3})=1$$

View Full Answer

Its FREE, you're just one step away


Single Correct Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86
Enroll Now For FREE

Realted Questions

Q1 Subjective Medium
Evaluate $$\int \dfrac{(\log x)^2}{x}dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Single Correct Medium
If $$y=\sqrt [ 4 ]{ { x }^{ 4 }-1 } $$ then $$\int { \frac { dx }{ \sqrt [ 4 ]{ { x }^{ 4 }-1 }  }  } $$ is equal to
  • A. $$-\frac { 3 }{ 4 } [log|\frac { y+1 }{ y-1 } |-{ Tan }^{ -1 }(y)]+c$$
  • B. $$-\frac { 1 }{ 2 } [log|\frac { y+x-1 }{ y-x+1 } |+{ Tan }^{ -1 }(y)]+c$$
  • C. $$-\frac { 3 }{ 8 } [log|\frac { y-x }{ y+x } |-{ Tan }^{ -1 }(\frac { y }{ x } )]+c$$
  • D. $$\frac { 1 }{ 4 } log|\frac { y-x }{ y+x } |-\frac { 1 }{ 2 } { Tan }^{ -1 }(\frac { y }{ x } )+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Subjective Medium
Solve  $$\int { \cfrac { x }{ { \left( 7x-10-{ x }^{ 2 } \right)  }^{ { 3 }/{ 2 } } } dx  } $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Medium
$$\displaystyle \overset{\pi/2}{\underset{0}{\int}}{ \dfrac { \sin ^6x }{ \cos ^{ 6 }{ x } +\sin ^{ 6 }{ x }  }  }dx$$ is equal to:
  • A. $$0$$
  • B. $$\pi$$
  • C. $$2\pi$$
  • D. $$\dfrac{\pi}{4}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 One Word Medium
Evaluate:$$\displaystyle \int \frac{dx}{\sqrt{16-x^{2}}}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer