Evaluate `underset (h to 0) lim ((a+h)^(2) sin (a+h) -a^(2) sin a)/h `.

Evaluate lim_(h to 0) ((a+h)^(2) sin (a+h) -a^(2) sin a)/h .

lim_(h rarr0)((a+h)^(2)sin(a+h)-a^(2)sin a)/(h)

The value of lim_(h rarr0)((a+h)^(2)sin(a+h)-a^(2)sin a)/(h)=

Evaluate lim_(h rarr0)((a+h)^(2)sin^(-1)(a+h)-a^(2)sin^(-1)a)/(h)

lim_(h rarr0)(sin h)/(h)

Evaluate underset( hrarr0 ) ( "Lim") ( ( x + h)^(sqrt( x+h))-x ^(sqrt( x)))/(h) ( x gt0)

Let fRtoR be a function we say that f has property 1 if underset(hto0)(lim)(f(h)-f(0))/(sqrt(|h|)) exist and is finite. Property 2 if underset(h to 0)(lim)(f(h)-f(0))/(h^(2)) exist and is finite. Then which of the following options is/are correct?