lim _x arrow 1 (x^4-√x)/(√x-1) is

Correct answer: (B) 7. lim _x arrow 1 (x^4-√x)/(√x-1)=lim _x arrow 1 (4 x^3-1/(2 √x))/(1/(2 √x))=lim _x arrow 1 ((8 x^3 √x-1)/(2 √4))/(1/(2 √x)) =7

Q102 / 180 · KCET 2025 · Mathematics

$\lim _{x \rightarrow 1} \frac{x^4-\sqrt{x}}{\sqrt{x}-1}$ is

A
$0$
Correct answer
B
$7$
C
Does not exist
D
$\frac{1}{2}$

Solution

$\begin{gathered}\lim _{x \rightarrow 1} \frac{x^4-\sqrt{x}}{\sqrt{x}-1}=\lim _{x \rightarrow 1} \frac{4 x^3-\frac{1}{2 \sqrt{x}}}{\frac{1}{2 \sqrt{x}}}=\lim _{x \rightarrow 1} \frac{\frac{8 x^3 \sqrt{x}-1}{2 \sqrt{4}}}{\frac{1}{2 \sqrt{x}}} \\ =7\end{gathered}$

Hence, the correct answer is option: 'B'.

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