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If lim(x->0)[1+x+(f(x))/x]^(1/x)=e^3, th...

If `lim_(x->0)[1+x+(f(x))/x]^(1/x)=e^3,` then find the value of `1n(lim_(x->0)[1+(f(x))/x]^(1/x))i s____`

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RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. If y=tan^(-1){(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))},"f i n d"(d...

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  2. The radius of the circle whose equation in parametric form is P(theta)...

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  3. If lim(x->0)[1+x+(f(x))/x]^(1/x)=e^3, then find the value of 1n(lim(x-...

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  4. Let log3^N = alpha1 + beta1 , log5^N = alpha2 + beta2 , log7^N = alph...

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  5. Consider curve y=f(x), then if PT = Length of tangent PN= Length of n...

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  6. If a chord of the circle x^(2)+y^(2)-4x-2y-c=0 is trisected at the poi...

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  7. If a x 62+b x+c=0 has imaginary roots and a-b+c >0 then the set of poi...

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  8. Evaluate: ("lim")(xvecoo)((a1^( 1/x)+a2^ (1/x)+ --+a n^(1/x))/n)^(n x)

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  9. Let a ray of light leaves the point (3, 4) reflects from the y-axis an...

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  10. If the line y=x cuts the curve x^3+3y^3-30 x y+72 x-55=0 in points A ,...

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  11. Find the equation of the bisector of the angle between the lines x+ 2...

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  12. Sum of roots of the equation x^2-2x^2sin^2(pix)/2+1=0 is 0 (b) 2 (...

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  13. DeltaABC is formed by the lines 2x-3y-6=0, 3x-y+3=0 and 3x+4y-12=0. If...

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  14. If the tangent at a point P with parameter t, on the curve x=4t^2+3, y...

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  15. The lines 3x+4y=9&4x-3y+12=0 intersect at Pdot The first line intersec...

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  16. If sum of the roots of the quadratic equation, a x^2+b x+c=0 is 12 , ...

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  17. If y= ln 5 (ln 7 x),then (dy)/(dx) =

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  18. The equation of the base of an equilateral triangle is x+y-2=0 and the...

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  19. The radius of a right circular cylinder increases at a constant rate. ...

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  20. If (x1-x2)^2+(y1-y2)^2=144 ,(x2-x3)^2+(y2-y3)^2=25 and (x3-x1)^2+(y3-y...

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