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If a function f(x) is defined by f(x) =`{((1+7x)^(1/x),when x!=0),(k,when x =0):}`is continuous at x = 0, then what is the value of k.?

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SHARAM PUBLICATION-MODEL QUESTION PAPER 13-EXERCISE
  1. Evaluate |[sin^2x, cos^2x,1],[cos^2x,sin^2x,1],[-10,12,2]|?

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  2. If underset(n)(I) is an identity matrix of order n, then k being a nat...

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  3. If a function f(x) is defined by f(x) ={((1+7x)^(1/x),when x!=0),(k,wh...

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  4. What is the maximum value of the function f(x)=sinx(1 + cos x) ?

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  5. Write the value of int0^(pi/2)(sinx)/(sinx+cosx)dx-int0^(pi/2)(cosx)/(...

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  6. If p and q are the order and degree of the differential equation y((dy...

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  7. Write the value of the cosine of the angle which the vector veca =hati...

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  8. Write the intercepts cutoff by the plane 2x+y-z =5 on three axes.

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  9. Show that the relation S in set A={x in Z : 0 le x le 12} given by S=...

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  10. Prove that tan^(-1)sqrt(x) =(1)/(2) cos^(-1)((1-x)/(1+x)), x in (0, 1)...

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  11. Solve: sin^(-1)((2a)/(1+a^2))+sin^(-1)((2b)/(1+b^2))=2tan^(-1)x.

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  12. Solve the following LPP graphically Maximize, Z=20x+30y Subject to...

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  13. Find the inverse of the matrix [[0,0,2],[0,2,0],[2,0,0]].

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  14. If A=[{:(3,-4),(1,-1):}] then show that A^(k)=[{:(1+2k,-4k),(k,1-2k):}...

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  15. Prove without expanding that |[bc,a,a^2],[ca,b,b^2],[ab,c,c^2]|=|[1,a^...

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  16. Solve : |[x-a, 0, 0],[a, x-b, 0],[a, b, x-c]|=0

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  17. Prove that: |[1, 1, 1],[a, b, c],[a^2, b^2, c^2]|=(a-b)(b-c)(c-a)

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  18. Find the value of k, so that the function defined by f(x)={(kx+1", if...

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  19. If x^y = e^(x-y) then prove that (dy)/(dx)=logx/(1+logx)^2.

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  20. If x=asec theta, y=b tan theta, then prove that (d^(2)y)/(dx^(2))=-(b^...

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