Evaluate \( \lim _{x \rightarrow 0} \frac{\sqrt{1+x^{3}}-\sqrt{1-x^{3}}}{x^{2}} \)

Channel:
Subscribers:
453,000
Published on ● Video Link: https://www.youtube.com/watch?v=hUM2pduOlMM



Duration: 2:44
1 views
0


Evaluate \( \lim _{x \rightarrow 0} \frac{\sqrt{1+x^{3}}-\sqrt{1-x^{3}}}{x^{2}} \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live




Other Videos By PW Solutions


2023-07-03Differentiate this function w.r.t \( x \frac{x^{4}+x^{3}+x^{2}+1}{x} \)
2023-07-03\( \lim _{x \rightarrow 0}\left(\sin m x \cot \frac{x}{\sqrt{3}}\right)=2 \), then \( m=\ldots . \).
2023-07-03Show that \( \lim _{x \rightarrow 4} \frac{|x-4|}{x-4} \) does not exist,
2023-07-03If \( f(x)=\frac{\tan x}{x-\pi} \) then \( \lim _{x \rightarrow \pi} f(x)= \)
2023-07-03\( \lim _{x \rightarrow \pi} \frac{1-\sin \frac{x}{2}}{\cos \frac{x}{2}\left(\cos \frac{x}{4}-\s...
2023-07-03Evaluate \( \lim _{x \rightarrow-3} \frac{x^{3}+27}{x^{5}+243}=\lim _{x \rightarrow-3} \frac{\fr...
2023-07-03Evaluate \( \lim _{x \rightarrow 0} \frac{1-\cos m x}{1-\cos n x} \)
2023-07-03If \( \lim _{x \rightarrow 1} \frac{x^{4}-1}{x-1}=\lim _{x \rightarrow k} \frac{x^{3}-k^{3}}{x^{...
2023-07-03Evaluate \( \lim _{x \rightarrow \pi / 6} \frac{\sqrt{3} \sin x-\cos x}{x-\frac{\pi}{6}} \)
2023-07-03Evaluate \( \lim _{x \rightarrow 1} \frac{x^{4}-\sqrt{x}}{\sqrt{x}-1} \)
2023-07-03Evaluate \( \lim _{x \rightarrow 0} \frac{\sqrt{1+x^{3}}-\sqrt{1-x^{3}}}{x^{2}} \)
2023-07-03Evaluate \( \lim _{x \rightarrow a} \frac{(2+x)^{5 / 2}-(a+2)^{5 / 2}}{x-a} \)
2023-07-03Evaluate \( \lim _{h \rightarrow 0} \frac{\sqrt{x+h}-\sqrt{x}}{h} \)
2023-07-03Evaluate \( \lim _{x \rightarrow 1 / 2} \frac{4 x^{2}-1}{2 x-1} \)
2023-07-03If \( f(x)=x^{100}+x^{99}+\ldots+x+1 \), then \( f^{\prime}(1) \) is equal to (a) 5050 (b) 5049 ...
2023-07-03If \( f(x)=\frac{x^{n}-a^{n}}{x-a} \) for some constant a, then \( f^{\prime}(a) \) is equal to ...
2023-07-03If \( f(x)=1+x+\frac{x^{2}}{2}+\ldots+\frac{x^{100}}{100} \), then \( f^{\prime}(1) \) is equal ...
2023-07-03Determine the points in (i) \( x y \)-plane (ii) \( y z \)-plane and (iii) \( z x \)-plane which...
2023-07-03Verify the following \( (5,-1,1),(7,-4,7),(1,-6,10) \) and \( (-1,-3,4) \) are the vertices of a...
2023-07-03\[ \lim _{x \rightarrow 0} \frac{\sqrt{\frac{1}{2}(1-\cos 2 x)}}{x}= \] (a) 1 (b) -1 (c) 0 (d) l...
2023-07-03The mid-points of the sides of a triangle \( A B C \) are given by \( (-2,3,5),(4,-1,7) \) and \...