Question

find out the lim of the given in the picture.​

Answer 1

Answer:

0

Step-by-step explanation:

cot x/4=cot45 =1

so,1-1/1+1-2=0/0=insoluble

Answer 2

Answer:

The value of the limit is : $\frac{3}{4}$

Step-by-step explanation:

$\\lim_{x \to\frac{\pi }{4} } \frac{cot^{3}x-1 }{cot^{3}x+cotx-2 }$

⇒$\lim_{x \to\frac{\pi }{4} }\frac{(cotx-1)(cot^{2}x+cotx+1) }{cot^{3}x-1+cotx-1 }$    [∵$x^{3}-y^{3}=(x-y)(x^{2}+xy+y^{2})$]

⇒$\lim_{x \to\frac{\pi }{4} }\frac{(cotx-1)(cot^{2}x+cotx+1)}{(cotx-1)(cot^{2}x+cotx+1)+1(cotx-1)}$

⇒$\lim_{x \to\frac{\pi }{4} }\frac{(cotx-1)(cot^{2}x+cotx+1)}{(cotx-1)(cot^{2}x+cotx+1+1)}$

⇒$lim_{x \to\frac{\pi }{4} }\frac{(cot^{2}x+cotx+1)}{(cot^{2}x+cotx+2)}$

now putting the limit, we get,

⇒$\frac{cot^{2}\frac{\pi }{4}+cot\frac{\pi }{4}+1}{cot^{2}\frac{\pi }{4}+cot\frac{\pi }{4}+2}$

⇒$\frac{1+1+1}{1+1+2}$       [∵$cot\frac{\pi }{4}=1$]

⇒$\frac{3}{4}$

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