यदि f एक समफलन है तब सिद्ध कीजिए कि `lim_(x to 0^(-))f(x)=lim_(x to 0^(+))f(x).`

If f is an even function, prove that lim_(xto0^(-)) (x)=lim_(xto0^(+)) f(x).

यदि f' (a) विधमान है तब lim_(x to a) (x f(a)-a f(x))/(x-a)=

The graph of y = f(x) is as shown in the following figure. Find the following values (i) f(-3)" "(ii) f(-2)" "(iii) f(0) (iv) f(2)" "(v) f(3)" "(vi) lim_(x to -3) f(x) (vii) lim_(x to 0) f(x)" "(viii)lim_(x to 2) f(x)" "(ix) lim_(x to 3) f(x) (x) lim_(x to 2^(-)) f(x)" "(x i)lim_(x to -2^(+)) f (x)" "(x ii)lim_(x to 0^(-)) f(x) (x iii) lim_(x to 0^(+)) f(x)

The graph of y = f(x) is as shown in the following figure. Find the following values (i) f(-3)" "(ii) f(-2)" "(iii) f(0) (iv) f(2)" "(v) f(3)" "(vi) lim_(x to -3) f(x) (vii) lim_(x to 0) f(x)" "(viii)lim_(x to 2) f(x)" "(ix) lim_(x to 3) f(x) (x) lim_(x to 2^(-)) f(x)" "(xi)lim_(x to -2^(+)) f (x)" "(x ii)lim_(x to 0^(-)) f(x) (x iii) lim_(x to 0^(+)) f(x)

The graph of y = f(x) is as shown in the following figure. Find the following values (i) f(-3)" "(ii) f(-2)" "(iii) f(0) (iv) f(2)" "(v) f(3)" "(vi) lim_(x to -3) f(x) (vii) lim_(x to 0) f(x)" "(viii)lim_(x to 2) f(x)" "(ix) lim_(x to 3) f(x) (x) lim_(x to 2^(-)) f(x)" "(xi)lim_(x to -2^(+)) f (x)" "(x ii)lim_(x to 0^(-)) f(x) (x iii) lim_(x to 0^(+)) f(x)

If f is an even function , then prove that Lim_( xto 0^(-)) f(x) = Lim_(x to 0^(+)) f(x) , whenever they exist .

Let f(x) is a function continuous for all x in R except at x = 0 such that f'(x) lt 0, AA x in (-oo, 0) and f'(x) gt 0, AA x in (0, oo) . If lim_(x rarr 0^(+)) f(x) = 3, lim_(x rarr 0^(-)) f(x) = 4 and f(0) = 5 , then the image of the point (0, 1) about the line, y.lim_(x rarr 0) f(cos^(3) x - cos^(2) x) = x. lim_(x rarr 0) f(sin^(2) x - sin^(3) x) , is

Let f(x) is a function continuous for all x in R except at x = 0 such that f'(x) lt 0, AA x in (-oo, 0) and f'(x) gt 0, AA x in (0, oo) . If lim_(x rarr 0^(+)) f(x) = 3, lim_(x rarr 0^(-)) f(x) = 4 and f(0) = 5 , then the image of the point (0, 1) about the line, y.lim_(x rarr 0) f(cos^(3) x - cos^(2) x) = x. lim_(x rarr 0) f(sin^(2) x - sin^(3) x) , is