Find the limits lim_{xrightarrow0}frac{sin x}{2x^2-x}

Find the limits lim_{xrightarrow0}frac{sin x}{2x^2-x}

Question
Limits and continuity
asked 2021-02-15
Find the limits
\(\lim_{x\rightarrow0}\frac{\sin x}{2x^2-x}\)

Answers (1)

2021-02-16
To evaluate: \(\lim_{x\rightarrow0}\frac{\sin x}{2x^2-x}\)
Solution:
\(\lim_{x\rightarrow0}\frac{\sin x}{2x^2-x}\)
On simplifying further, we get:
\(\lim_{x\rightarrow0}\frac{\sin x}{2x^2-x}=\lim_{x\rightarrow0}\frac{\sin x}{x(2x-1)}\)
\(=\lim_{x\rightarrow0}\frac{\sin x}{x}\times\frac{1}{(2x-1)}\)
\(=\lim_{x\rightarrow0}1\times\frac{1}{(2x-1)}\)
\(=\frac{1}{2(0)-1}\)
\(=\frac{1}{-1}\)
\(=-1\)
Result:
\(\lim_{x\rightarrow0}\frac{\sin x}{2x^2-x}=-1\)
0

Relevant Questions

asked 2020-12-24
Find the limits
\(\lim_{x\rightarrow0}\sin(\frac{\pi+\tan x}{\tan x-2\sec x})\)
asked 2020-11-26
Use Taylor series to evaluate the following limits.
\(\lim_{x\rightarrow0}\frac{\sqrt{1+2x}-1-x}{x^2}\)
asked 2020-10-27
Use L'Hospital Rule to find the limits
\(\lim_{x\rightarrow0}\frac{\sin mx}{\sin nx}\)
asked 2021-02-19
Evaluate the following limits.
\(\lim_{x\rightarrow0}\frac{\tan7x}{\sin x}\)
asked 2021-01-15
Suppose the functions f(x) and g(x) are defined for all x and that \(\lim_{x\rightarrow0}f(x)=\frac{1}{2}\) and \(\lim_{x\rightarrow0}g(x)=\sqrt2\). Find the limits as \(x\rightarrow0\) of the following functions. \(f(x)\frac{\cos x}{x-1}\)
asked 2021-01-31
Find the limits. Write \(\infty\) or \(-\infty\) where appropriate. \(\lim_{x\rightarrow0^-}\frac{x^2-3x+2}{x^3-4x}\)
asked 2021-01-31
Use Taylor series to evaluate the following limits.
\(\lim_{x\rightarrow0}\frac{\sec x-\cos x-x^2}{x^4} \ (Hint: \text{The Maclaurin series for sec x is }1+\frac{x^2}{2}+\frac{5x^4}{24}+\frac{61x^6}{720}+...)\)
asked 2020-12-05
Use L'Hospital Rule to evaluate the following limits.
\(\lim_{x\rightarrow0}\frac{\tanh^{-1}x}{\tan(\pi x/2)}\)
asked 2021-02-23
Use Taylor's theorem to evaluate the following limits. \(\lim_{x\rightarrow0}\frac{3\sin^2(x)+2\sin^4(x)}{3x\tan(x)}\)
asked 2020-10-26
Use Taylor's theorem to evaluate the following limits. \(\lim_{x\rightarrow0}\frac{x\sin(x)-x^2}{\cos(x)-1+\frac{x^2}{2}}\)
...