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If : f(x) {:(=x^(2)", ... "x...

If : f(x) `{:(=x^(2)", ... "x le 1 ),(= x+5 ", ... "x gt 1 ):}` then :

A

f(x) is continuous at x = 1

B

f(x) is discontinuous at x =1

C

` lim _( x to 1) f(x) =1`

D

none of these

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Verified by Experts

The correct Answer is:
b
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MARVEL PUBLICATION-CONTINUITY F FUNCTIONS-MULTIPLE CHOICE QUESTIONS
  1. Let : f(x) {:(=(1-cos 4x)/(x^(2))", ... "x lt 0 ),(= a", ...

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  2. If : f(x) {:(=ax^(2)-b", ... " 0 le x lt 1 ),(=2", ...

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  3. If : f(x) {:(=x^(2)", ... "x le 1 ),(= x+5 ", ... "...

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  4. If : f(x) {: (=(x^(2)+3x-10)/(x^(2)+2x-15)", ... "x!= -5 ),(=a", ...

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  5. If : f(x) {:( =x+lambda", ... " x lt 3),(=4", ... " ...

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  6. If the function f(x) {:(= 1+sin. ((pix)/2)", ..." -ooltxle1 ),(=...

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  7. The function f(x) {:(= x+2", ... " 1 lex le 2 ),(=4 ", ...

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  8. In order that the function f(x) = (x+1)^(cot x) is continuous at x=0 ,...

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  9. f:R->R is defined by f(x)={(cos3x-cosx)/(x^2), x!=0lambda, x=0 and f ...

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  10. Function f(x) = (1-cos 4x)//(8x^(2)), " where " x != 0 , and f(x) = k...

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  11. If : f(x) {: ((1-sin x)/(pi-2x)", ... " x != pi//2 ),(=lambda ",...

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  12. If f(x)=(sqrt(a^2-a x+x^2)-sqrt(a^2+a x+x^2))/(sqrt(a+x)-sqrt(a-x)) is...

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  13. If S(1)= sum(r=1)^(n) r , S(2) = sum(r=1)^(n) r^(2),S(3) = sum(r=1)^(n...

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  14. underset(x to (pi)/(2))(lim)(a^(cot x) -a^(cosx))/(cot x- cot x ) is ...

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  15. lim (x to oo) (1-4/(x-1))^(3x-1)=

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  16. If alpha is not an integral multiple of pi , then : lim(x to alpha)...

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  17. lim(h -> 0) (sin(a+3h)-3sin(a+2h)+3sin(a+h)-sina)/h^3 =

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  18. lim (x to n ) (-1)^([x])=

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  19. Evaluate: ("lim")(hvec0)(2[sqrt(3)sin(pi/6+h)-cos(pi/6+h)])/(sqrt(3)h(...

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  20. If f(x) = 0 is a quadratic equation such that f(-pi) =f(pi) = 0 and f(...

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