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Evaluate underset(xrarr0)"lim" f(x), whe...

Evaluate `underset(xrarr0)"lim" f(x)`, where

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Evaluate lim_(xrarr0) f(x) , where

Consider the function: f(x)={{:((alphacosx)/(pi-2x),"if "xne(pi)/(2)),(3,"if "x=(pi)/(2)):} Which is continuous at x=(pi)/(2) , where alpha is a constant. What is underset(xrarr0)(lim)f(x) equal to?

Consider the following statements in respect of the function f(x)=sin((1)/(x)) for xne0 and f(0)=0 1. underset(xrarr0)lim f(x) exists 2. f(x) is continuous at x = 0 Which of the above statements is/are correct?

Consider the following statements: I. underset(xrarr0)lim (x^(2))/(x) exists. II. ((x^(2))/(x)) is not continuous at x = 0. III. underset(xrarr0)(lim)(|x|)/(x) does not exist Which of the above statements are correct?

Find lim_(xrarr5) f(x) , where f(x)=|x|-5 .

The value of lim_(xrarr0)[(x)/(sinx)] , where [.] represents the greatest integer function,is

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MAHAVEER PUBLICATION-LIMITS-QUESTION BANK
  1. Find lim(x rarr pi){sin(x- pi)}/{(pi(pi-x)}

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  2. Find lim(x rarr 0) f(x) where f(x) = {(2x+3,xle0),(3(x+1),xgt0):}

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  3. Evaluate underset(xrarr0)"lim" f(x), where

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  4. Suppose f(x)={(a+bx, x<1), (4, x=1), (b-ax, x>1):} and if lim(xto1) f(...

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  5. If the function f(x) satisfies (lim)(x->1)(f(x)-2)/(x^2-1)=pi,evaluate...

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  6. Evaluate the following limits : lim(x rarr 1) {2(x+3)+7}

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  7. Evaluate the following limits : lim(x rarr 1) (3x + 1) (x+ 1)

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  8. Evaluate the following limits : lim(x rarr -1) (x+1)/(x+2)

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  9. Evaluate the following limits : lim(x rarr 0) (px + q)/(ax + b)

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  10. underset(xrarr-2)"lim"((1)/(x)+(1)/(2))/(x+2)

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  11. Evaluate the following limits: lim(xto-2)((x^(2)-25)/(x-5))

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  12. Evaluate the following limits : lim(x rarr 1/3) (9x^2-1)/(3x-1)

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  13. Evaluate the following limits : lim(x rarr 2) (x^2-x-2)/ (x^2-3x+2)

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  14. Evaluate the following limits : lim(x rarr 1) [1/(x-1)-2/(x^2-1)]

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  15. Evaluate the following limits : lim(x rarr 2) (sqrt(3x-2) -x)/(2-sqr...

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  16. Evaluate the following limits : lim(x rarr 0) x/(5-|x|)

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  17. Evaluate the following limits : lim(x rarr -2) (x^11-1)/(x^7 -1)

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  18. (lim)(x->0)(cosx)/(pi-x)

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  19. (lim)(x->0)(cos2x-1)/(cosx-1)

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  20. lim(x->0)(sina x+b x)/(a x+sinb x)

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