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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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  8. Evaluate the following limit: lim(x->pi/3)(sqrt(3)-t a n x)/(pi-3x)

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  9. Evaluate the following limit: lim(x->pi//2)(sqrt(2)-sqrt(1+sin x))/(co...

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  10. Evaluate the following limit: lim(x->pi/4)(sqrt(2)-cos x-sin x)/((pi/4...

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  11. Evaluate the following limit: lim(x->a)(cos x-cos a)/(sqrt(x)-sqrt(a))

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  12. Evaluate the following limit: lim(x->a)(cossqrt(x)-cossqrt(a))/(x-a)

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  13. Evaluate the following limit: lim(x->1)(1+cospix)/((1-x)^2)

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  14. Evaluate lim(x->pi/4)(1-sin2x)/(1+cos4x)

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  15. Evaluate: (lim(n->oo)ncos(pi/(4n))sin(pi/(4n))

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  16. Evaluate the following limit: lim(n->oo)(sin(a/(2^n)))/(sin(b/(2^(n\ )...

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  17. Evaluate the following limit: lim(x->2)(x^2-x-2)/(x^2-2x+"sin"(x-2))

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  18. lim(x->1)(1-x)tan(pix)/2=

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

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  20. Evaluate the following limit: lim(x->1)(1-1/x)/(sinpi(x-1))

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