`f(x)={(2/(5-x), xlt3), (5-x , xgeq3):}` discuss `lim_(x->3) f(x)`

f(x)={(x+1,; xlt1), (2x-3,; xgeq1):}, evaluate lim_(x rarr 1)f(x).

If f(x)={(x^2+2,,,xge2),(1-x ,,,xlt2):} ; g(x)={(2x,,,xgt1),(3-x ,,,xle1):} then the value of lim_(x->1) f(g(x)) is

If f(x)={(x^2+2,,,xge2),(1-x ,,,xlt2):} ; g(x)={(2x,,,xgt1),(3-x ,,,xle1):} then the value of lim_(x->1) f(g(x)) is

Let f(x) =[{:(asqrt(x+1),0lt xlt3),(bx +2, 3lexlt5):} if f(x) is differentiable at x=3 then find the values of a and b.

The function f is defined by f(x)={{:(x+3" if ",xlt1),(x^(2)" if ",xge1):} . Find f(-5),f(1), and f(3) .

If f(x) is defined as f(x)={{:(2x+3,x,le 0),(3x+3,x,ge 0):} then evaluate : lim_(xrarr0) f(x) "and" lim_(xrarr1) f(x)

If lim_(x->oo) f(x) exists and is finite and nonzero and if lim_(x->oo) {f(x)+(3f(x)−1)/(f^2(x))}=3 ,then the value of lim_(x->oo) f(x) is

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)