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f(x) = {(|x+1|/(x+1),when x!= -1),(0, wh...

f(x) = `{(|x+1|/(x+1),when x!= -1),(0, when x = -1):}`
Test whether f(x) is continuous or not at x= -1

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A function f (x) is defined as followes: f(x)={{:(xsin.(1)/(x),"when " xne0),(0,"when " x=0):} Show that f (x) is continuous at x =0 .

If f(x)={{:(x+sinx,"when "xlt0),(0,"when "xge0):} examine whether f(x) is continuous at x = 0.

If f(x) = {(|sinx|/x, when x=0),(1, when x!=0):} then examine the continuity of the function at x=0.

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Let f(x)={(x exp[-(1/|x|+1/x)], x ne 0),(0, x=0):} Test whether f(x) is differentiable at x=0

If f(x)={(|x|-3 when x = 1) & g(x)={2-|x| when x = 2 . if h(x)=f(x)+g(x) is discontinuous at exactly one point, then - (a). a=-3, b=0 (b). a=-3, b=-1 (c) a=2, b=1 (d) a=0, b=1

UNITED BOOK HOUSE-SET 4-EXERCISE
  1. answer any one question A=[[1,0],[-1,7]] and I be the unit matrix of s...

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  2. Without expanding show that |[1/a,1,bc],[1/b,1,ca],[1/c,1,ab]|=0

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  3. f(x) = {(|x+1|/(x+1),when x!= -1),(0, when x = -1):} Test whether f(...

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  4. Find the value of c that occurs in the conclusion of lagrange's MVT in...

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  5. Solve: (x-y)(dx+dy) = dx-dy when x= 0, y = -1

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  6. For any two vectors veca and vec b show that |vec a.vec b|le |vec a|.|...

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  7. Show that the condition for the lines x= a1z+b1,y = c1z+d1 and x = a2z...

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  8. Can the two events A and B be mutually exclusive if P(A) = 1/8,P(A//B)...

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  9. Let * be a binary operation defined by a* b = L.C.M , (a,b) AA a,b in ...

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  10. Solve: sin^-1x+sin^-1(1-x)=cos^-1x

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  11. Show that, A = 1/3[[1,2,2],[2,1,-1],[-2,2,-1]] are orthogonal matrix a...

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  12. Prove that |[x,a,b],[a,x,b],[a,b,x]|=(x-a)(x-b)(x+a+b)

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  13. Prove that |[b+c ,a-b, a] ,[c+a, b-c ,b],[ a+b, c-a, c]|=3abc-a^3-b^3-...

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  14. If y = sin^(-1){(5x+12sqrt(1-x^2))/13} then show that (dy)/(dx) = 1/sq...

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  15. If (sqrt(1-x^2))y= sin^(-1)x then show that (1-x^2)y2-3xy1-y =0

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  16. Evaluate: int(sin^(-1)x)/(1-x^2)^(3//2)dx

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  17. Evaluate: int (dx)/sqrt(2/3x^3-x^2+1/3)

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  18. Solve: x(dy)/(dx)+3y = x^2

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  19. Solve: (x^2+y^2)dy-xydx=0

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  20. If 2vec a+ 3vecb + vec c = vec 0, then show that vec axxvec b+vec bxxv...

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