[" 29.If "f" be a real valued function defined on the interval "(0,oo)],[" by "f(x)=ln x+int_(0)^(x)sqrt(1+sin t)dt" .Then,which of the "],[" following statement (s) is (are) correct? "],[" (a) "f''(x)" exists for all "x in(0,oo)],[" (b) "f'(x)" but not differentiable on "(0,oo)],[" (c) there exists "alpha>1" such that "|f'(x)|<|f(x)|" for all "],[" (d) there exists "beta>0" such that "|f(x)|+|f'(x)|<=beta" fror "],[" all "x in(0,oo)]

Let f be a real valued function defined on the interval (0,oo) by f(x)=In x+int_(0)^(x)sqrt(1+sint)dt . Then which of the following statement (s) is (are) true?

Let f be a real-valued function defined on interval (0,oo),by f(x)=lnx+int_0^xsqrt(1+sint).dt. Then which of the following statement(s) is (are) true? (A). f"(x) exists for all in (0,oo)." " (B). f'(x) exists for all x in (0,oo) and f' is continuous on (0,oo), but not differentiable on (0,oo)." " (C). there exists alpha>1 such that |f'(x)|<|f(x)| for all x in (alpha,oo)." " (D). there exists beta>1 such that |f(x)|+|f'(x)|<=beta for all x in (0,oo).

Let f be a real-valued function defined on interval (0,oo) ,by f(x)=lnx+int_0^xsqrt(1+sint).dt . Then which of the following statement(s) is (are) true? (A). f"(x) exists for all in (0,oo) . " " (B). f'(x) exists for all x in (0,oo) and f' is continuous on (0,oo) , but not differentiable on (0,oo) . " " (C). there exists alpha>1 such that |f'(x)|<|f(x)| for all x in (alpha,oo) . " " (D). there exists beta>1 such that |f(x)|+|f'(x)|<=beta for all x in (0,oo) .

Let f be a real-valued function defined on interval (0,oo) ,by f(x)=lnx+int_0^xsqrt(1+sint).dt . Then which of the following statement(s) is (are) true? (A). f"(x) exists for all in (0,oo) . " " (B). f'(x) exists for all x in (0,oo) and f' is continuous on (0,oo) , but not differentiable on (0,oo) . " " (C). there exists alpha>1 such that |f'(x)|<|f(x)| for all x in (alpha,oo) . " " (D). there exists beta>1 such that |f(x)|+|f'(x)|<=beta for all x in (0,oo) .

Let f be a real-valued function defined on interval (0,oo) ,by f(x)=lnx+int_0^xsqrt(1+sint).dt . Then which of the following statement(s) is (are) true? (A). f"(x) exists for all in (0,oo) . " " (B). f'(x) exists for all x in (0,oo) and f' is continuous on (0,oo) , but not differentiable on (0,oo) . " " (C). there exists alpha>1 such that |f'(x)|<|f(x)| for all x in (alpha,oo) . " " (D). there exists beta>1 such that |f(x)|+|f'(x)|<=beta for all x in (0,oo) .

Let f:[0,oo)rarrR be a continuous function such that f(x)=1-2x+int_(0)^(x)e^(x-t)f(t)dt" for all "x in [0, oo). Then, which of the following statements(s) is (are)) TRUE?

Let f:[0,oo)rarrR be a continuous function such that f(x)=1-2x+int_(0)^(x)e^(x-t)f(t)dt" for all "x in [0, oo). Then, which of the following statements(s) is (are)) TRUE?

The function f : (0, oo) rarr [0, oo), f(x) = (x)/(1+x) is

The function f : (0, oo) rarr [0, oo), f(x) = (x)/(1+x) is