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Evaluate the following limit: lim(x->pi)...

Evaluate the following limit: `lim_(x->pi)(1+cos x)/(tan^2x)`

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`lim_(x->pi)(1+cos x)/(tan^2x)`
`=lim_(x->pi)(1+cos x)/((sin^2x)/(cos^2x))`
`=lim_(x->pi)((1+cos x)/(sin^2x)xx cos^2x) `
`=lim_(x->pi)((1+cos x)/(1-cos^2x)xx cos^2x) `
`=lim_(x->pi)((1+cos x)/((1-cosx)(1+cosx))xx cos^2x) `
`=lim_(x->pi) ((cos^2x)/(1-cosx))`
`=(cos^2pi)/(1-cos pi)`
`=1/2`
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RD SHARMA-LIMITS-All Questions
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  3. Evaluate the following limit: lim(x->pi)(1+cos x)/(tan^2x)

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  4. Evaluate the following limit: lim(x->pi/6)(cot^2x-3)/(cos e c x-2)

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  5. Evaluate the following limit: lim(x->pi/4)(2-cos e c^2x)/(1-cot x)

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  6. The value of lim(x->pi) (sqrt(2+cosx)-1)/(x-pi)^2

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  7. Evaluate the following limit: lim(x->(3pi)/2)(1+cos e c^3x)/(cot^2x)

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  10. Evaluate the following limit: lim(x->0)(a^x+b^x-2)/(x^(2\ ))

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  11. Evaluate the following limit: lim(x->0)(8^x-4^x-2^x+1)/(x^2)

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  12. Evaluate the following limit: lim(x->0)(5^x+3^x+2^x-3)/x

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  13. Evaluate the following limit: lim(x->0)(e^x-1+sin x)/x

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  14. Evaluate the following limit: lim(x->0)(e^(sinx)-1)/x

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  16. Evaluate: lim(x->a)(logx-loga)/(x-a)

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  20. Evaluate the following limit: (lim))("log"(1+x))/(3^x-1)

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