Evaluate lim x - 0x-15-1-x

We have,Evaluate lim_x→ 0(x+1)^5 1/x At x=0,the value of the expression is 0/0 form. Applying L'Hospital Rule =lim_x→ 0 { (x+1)^5 1 } =lim_x→ 05(x+1)^4 × 1 0/1 ...

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Byju's Answer

Standard XII

Mathematics

L'Hospital Rule to Remove Indeterminate Form

Evaluate lim ...

Question

Evaluate $lim x \to 0 \frac{(x + 1)^{5} - 1}{x}$
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Solution

We have,Evaluate $lim x \to 0 \frac{(x + 1)^{5} - 1}{x}$

At x=0,the value of the expression is $\frac{0}{0}$ form.

Applying L'Hospital Rule

$= lim x \to 0$ ${(x + 1)^{5} - 1}$

$= lim x \to 0 \frac{5 (x + 1)^{4} \times 1 - 0}{1}$

$= lim x \to 0 5 (x + 1)^{4}$

Putting x=0

= $5 (1)^{4} = 5$

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Evaluate limx→0(x+1)5−1x ___

We have,Evaluate limx→0(x+1)5−1x At x=0,the value of the expression is 00 form. Applying L'Hospital Rule =limx→0 {(x+1)5−1} =limx→05(x+1)4×1−01 =limx→05(x+1)4 Putting x=0 =5(1)4=5

Evaluate $lim x \to 0 \frac{(x + 1)^{5} - 1}{x}$
___

We have,Evaluate $lim x \to 0 \frac{(x + 1)^{5} - 1}{x}$

At x=0,the value of the expression is $\frac{0}{0}$ form.

Applying L'Hospital Rule

$= lim x \to 0$ ${(x + 1)^{5} - 1}$

$= lim x \to 0 \frac{5 (x + 1)^{4} \times 1 - 0}{1}$

$= lim x \to 0 5 (x + 1)^{4}$

Putting x=0

= $5 (1)^{4} = 5$