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If f(x)={{:(mx^(2)+n",", x lt 0), (nx+m...

If `f(x)={{:(mx^(2)+n",", x lt 0), (nx+m",", 0 le x le 1), (nx^(3)+m",", x gt 1):}`. For what integers `m` and `n` does `lim_(x to 0)f(x)" and "lim_(x to 1)f(x)` exist ?

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MODERN PUBLICATION-LIMITS AND DERIVATIVES-NCERT FILE - EXERCISE 13.1
  1. underset(xrarr0)"lim"(sinax)/(bx)

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  2. Evaluate the following limits lim(x to 0)(sinax)/(sinbx), a,b ne 0.

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  3. (lim)(x->pi)(sin(pi-x))/(pi(pi-x))

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  4. underset(xrarr0)"lim"(cos x)/(pi-x)

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  5. underset(xrarr0)"lim"(cos 2x-1)/(cos x-1)

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  6. Evaluate the following limits in Exercise 1 to 22. lim(a to 0)(ax+xc...

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  7. Evaluate the following limits in Exercise 1 to 22. lim(x to 0)xsecx.

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  8. underset(xrarr0)"lim"(sinax+bx)/(ax+si nbx),a,b,a+bne0

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  9. underset(xrarr0)"lim"(cosecx-cotx)

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  10. underset(xrarr(pi)/(2))"lim"(tan2x)/(x-(pi)/(2))

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  11. Find lim(x to 0)f(x) and lim(x to 1)f(x), where f(x)={{:(2x+3",", x ...

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

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  13. Evaluate ("lim")(x->0)f(x),\ w h e r e\ f(x)={(|x|)/x ,\ x!=0 0,\ x=0

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  14. Find lim(x to 0) f(x), where f(x)={{:( x/abs "x " " ,", x ne 0), ...

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

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

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  17. Let a(1),a(2),...,a(n) be fixed real numbers and let f(x)=(x-a(1))(...

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  18. Let 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(x to 1) (f(x)-2)/(x^(2)-1)=pi, then...

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  20. If f(x)={{:(mx^(2)+n",", x lt 0), (nx+m",", 0 le x le 1), (nx^(3)+m",...

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