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Consider the function, f defined by f(x)=| x − 3| + [x] x ∈ [2,4] where x] denotes the greatest integer function. Is this function differentiable in ?[2,4]Justify your answer
Show that Rn(x) the Lagrange’s form of remainder in the Maclaurin series expansion of cos 3x tends to zero as n → ∞.Hence obtain its infinite Maclaurin expansion.
Prove that "\\lim _{x\\to \\infty }\\left(\\left(\\frac{1}{\\left(x+5\\right)^2}\\right)\\right)" = inf with proper justification.
For the function f defined by f(x)= 3x − 2 over [0,1] , verify L(P, f)<=U(P, f)( where the partition P is = "\\left(0,\\frac{1}{3},\\frac{2}{3},1\\right)".
Show that the function f defined on [1,0] by f(x) = (-1)n-1 for 1/n+1 <x< = 1/n (for n= 1,2,3,...) is integrable on [0,1]
Examine the following series for convergence: "\\sum _{n=0}^{\\infty }\\left(\\frac{n-2}{2n+3}\\right)^n"
find "\\lim _{n\\to \\infty }\\left(\\frac{1}{\\left(2n+1\\right)^2}+\\frac{2}{\\left(2n+2\\right)^2}\\frac{3}{\\left(2n+3\\right)^2}\\right)+...+\\frac{3}{25n}"
If the power series {summation} an xn converges uniformly in ] α ,β [ then so does {summation} an (-x)n . true or false ? Justify
Check whether the series {Summation} n2x5/(n4+x3) , x belongs to [0, a] is uniformly convergent or not ,where a belongs to R
Prove that every continuous function on (a, b) is integrable
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