[" n defined on the interval "(0,oo)" by "f(x)=ln x+int_(0)^(1)sqrt(1+sin t)" dt.Then which "],[" is (are) true? "],[" of "],[" of "f" ' is continuous on "(0,oo)" ,but not differentiable on "(0,oo)],[" hat "|f'(x)|<|f(x)|" for all "x in(alpha,oo)],[" hat "|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 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 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:(-oo,oo)to(-oo,oo) be defined by f(x)=x^(3)+1 Statement - I : The function f has a local exremum at x=0 Statement 2 : The function f is continuous and differentiable on (-oo,oo)andf(0)=0

Let f:(0,oo) in R be given f(x)=int_(1//x)^(x) e^-(t+(1)/(t))(1)/(t)dt , then

f : R to (0, oo) defined by f (x) = log _(2) (x). then f ^-1(x)