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Consider the function f(x)={(1-a^x+x a^x...

Consider the function `f(x)={(1-a^x+x a^x ln a)/(a^xx^2); x<0(2^xa^x-x ln2-x ln a-1)/(x^2); x >0` where `a > 0.` If `g(x)` is continuous at `x=0` then `a=sqrt(2)` (b) `g(0)=1/8(ln2)^2` `a=1/(sqrt(2))` (d) `g(0)=1/2ln2`

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RESONANCE DPP-JEE MAINS-All Questions
  1. Which of the following is/are correct? If vec a= hat i+ hat j and ve...

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  2. Suppose a1,a2, real numbers, with a1!=0, If a1,a2,a3 are in AdotPdo...

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  3. Consider the function f(x)={(1-a^x+x a^x ln a)/(a^xx^2); x<0(2^xa^x-x ...

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  4. A triangle has two of its sides along the lines y=m1x&y=m2x where m1, ...

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  5. The three vectors hat i+ hat j , hat j+ hat k , hat k+ hat i taken tw...

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  6. The number of integer values of m , for which the x-coordinate of the ...

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  7. If A^2+A+I=0 , then A is non-singular A!=0 (b) A is singular A^(-...

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  8. Tangent and normal to the curve y=2s in x+s in2x are drawn at p(x=pi/3...

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  9. If D=|[1/z,1/z,-(x+y)/(z^2)],[-(y+z)/(x^2),1/x,1/x],[-(y(y+z)/(x^2z))...

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  10. The curve y=x^3+x^2-x has two horizontal tangents. The distance betwee...

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  11. The exhaustive domain of f(x)=sqrt(x^(12)-x^9+x^4-x+1) is

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  12. The point of intersection of tangent to the curve y=x^4 at (1,1) with ...

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  13. Equation of straight line a x+b y+c=0 , where 3a+4b+c=0 , which is at ...

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  14. Tangents are drawn from the point P(1,-1) to the circle x^2+y^2-4x-6y-...

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  15. If A=[(1,2,2),(2,1,2),(2,2,10] then (A) A^-1= 1/5(A-4I3) (B) A^2-4A-5I...

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  16. The derivative of (log)(10)x w.r.t. x^2 is equal to 1/(2x^2)loge 10 (...

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  17. If A=[1 2 0-1 1 2 2-1 1],t h e ndet(A d j(A d jA))= 13 (b) 13^2 (c) ...

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  18. Which of the following limits tends to unity? (a) ("lim")(xvec0)sin(ta...

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  19. The algebraic sum of the perpendicular distances from A(x1, y1), B(x2,...

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  20. If sum(k=1)^(k=n)tan^(- 1)(2k)/(2+k^2+k^4)=tan^(- 1)(6/7), then the va...

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