Answered

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Limit as x approaches 0 of (sin^2x)/x

Sagot :

abidemiokin

Answer:

0

Step-by-step explanation:

Given the expression

[tex]\lim_{x \to \ 0} \frac{sin^2x}{x}[/tex]

Substitute the value of x in the function

[tex]= \frac{sin ^2(0)}{0}\\= 0/0 (indeterminate) \\[/tex]

Apply l'hospital rule

[tex]\lim_{x \to \ 0} \frac{d/dx(sin^2x)}{d/dx(x)} \\= \lim_{x \to \ 0} \frac{(2sinxcosx)}{1} \\[/tex]

Substitute the value of x

= 2 sin(0)cos(0)

= 2 * 0 * 1

= 0

Hence the limit of the function is 0

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