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If f(x)={{:(|x|+1",",xlt0),(0",",x=0),(|...

If `f(x)={{:(|x|+1",",xlt0),(0",",x=0),(|x|-1",",xgt0):}`
For what value(s) of a does `lim_(xrarra)f(x)` exists?

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The correct Answer is:
`lim_(xrarra)f(x)` exists for all `ane0`.
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NCERT GUJARATI-LIMITS AND DERIVATIVES-EXERCISE 13.1
  1. Evaluate the following limits in lim(xrarr0)(sinax)/(bx)

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  2. Evaluate the following limits in lim(xrarr0)(sinax)/(sinbx),a,b ne0

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  3. Evaluate the following limits in lim(xrarrpi)(sin(pi-x))/(pi(pi-x))

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  4. Evaluate the following limits in lim(xrarr0)(cosx)/(pi-x)

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  5. Evaluate the following limits in lim(xrarr0)(cos2x-1)/(cosx-1)

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  6. Evaluate the following limits in lim(xrarr0)(ax+x cosx)/(b sinx)

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  7. Evaluate the following limits in lim(xrarr0)x secx

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  8. Evaluate the following limits in lim(xrarr0)(sinax+bx)/(ax+sinbx)a,b...

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  9. Evaluate the following limits in lim(xrarr0)("cosec "x-cotx)

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  10. Evaluate the following limits in lim(xrarr(pi)/(2))(tan2x)/(x-(pi)/(...

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  11. Find lim(xrarr0)f(x) and lim(xrarr1)f(x), where f(x)={{:(2x+3",",xle0)...

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  12. Find lim(xrarr1)f(x), where f(x)={{:(x^(2)-1",",xle1),(-x^(2)-1",",xgt...

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  13. Evaluate lim(xrarr0)f(x)," where "f(x)={{:((|x|)/(x)",",x ne0),(0",",x...

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  14. Find lim(xrarr0)f(x), where f(x)={{:((x)/(|x|)",", x ne0),(0",",x=0):}

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

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  16. Suppose f(x)={{:(a+bx",",xlt1),(4",",x-1),(b-ax",",xgt1):} and if li...

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  17. Let a(1), a(2),…,a(n) be fixed real numbers and define a function f(x)...

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  18. If f(x)={{:(|x|+1",",xlt0),(0",",x=0),(|x|-1",",xgt0):} For what val...

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  19. If the function f(x) satisfies lim(xrarr1)(f(x)-2)/(x^(2)-1)=pi, evalu...

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  20. If f(x)={{:(mx^(2)+n",",xlt0),(nx+m",",0lexle1),(nx^(3)+m",",xgt1):}. ...

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