Let f (x)= {{:(((e ^(1/(x-2))-3))/((1)/(...

Let f (x)= `{{:(((e ^(1/(x-2))-3))/((1)/(3 ^(x-2))+1), x gt 2), ((b sin{-x})/({-x}), x lt 2),(c, x=2):},` where {.} denotes fraction part function, is continuous at `x=2,` then `b+c=`

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VK JAISWAL ENGLISH-CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION-EXERCISE (SUBJECTIVE TYPE PROBLEMS)

Let f (x)= {{:(((e ^(1/(x-2))-3))/((1)/(3 ^(x-2))+1), x gt 2), ((b sin...
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Let f (x)= {{:(ax (x-1)+b,,, x lt 1),( x+2,,, 1 le x le 3),(px ^(2) +q...
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If y= sin (8 sin ^(-1) x ) then (1-x ^(2)) (d^(2)y)/(dx ^(2))-x (dy)/...
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If y ^(2) =4ax, then (d^(2) y)/(dx ^(2))=(ka ^(2))/( y ^(2)), where k ...
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The number of values of x , x ∈ [-2,3] where f (x) =[x ^(2)] sin (pix)...
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If f (x) is continous and differentiable in [-3,9] and f'(x) in [-2,8]...
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In f (x)= [{:(cos x ^(2),, x lt 0), ( sin x ^(3) -|x ^(3)-1|,, x ge 0)...
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Consider f(x) =x^(2)+ax+3 and g(x) =x+band F(x) = lim( n to oo) (f...
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Let f (x)= {{:(2-x"," , -3 le x le 0),( x-2"," , 0 lt x lt 4):} Then f...
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If f (x) +2 f (1-x) =x ^(2) +2 AA x in R and f (x) is a differentiable...
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Let f (x)= signum (x) and g (x) =x (x ^(2) -10x+21), then the number o...
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If (d^(2))/(d x ^(2))((sin ^(4)x+ sin ^(2)x+1)/(sin ^(2)x + si n x+1))...
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f (x) =a cos (pix)+b, f'((1)/(2))=pi and int (1//2)^(3//2) f (x) dx =2...
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Let alpha (x) = f(x) -f (2x) and beta (x) =f (x) -f (4x) and alpha '(1...
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Let f (x) =-4.e ^((1-x)/(2))+ (x ^(3))/(3 ) + (x ^(2))/(2)+ x+1 and g ...
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If y=3^(2 sin ^(-1)) then |((x ^(2) -1) y^('') +xy')/(y)| is equal to
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Let f (x)=x+ (x ^(2))/(2 )+ (x ^(3))/(3 )+ (x ^(4))/(4 ) +(x ^(5))/(5)...
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In f (x)= [{:(cos x ^(2),, x lt 0), ( sin x ^(3) -|x ^(3)-1|,, x ge 0)...
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For the curve sinx+siny=1 lying in first quadrant. If underset(xrarr0...
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Let f (x) = x tan ^(-1) (x^(2)) + x^(4) Let f ^(k) (x) denotes k ^(th)...
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If x = cos theta and y = sin^(3) theta, then |(yd ^(2)y)/(dx ^(2))+((d...
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