Evaluate :
`lim_( h -> 1 ) ( h -1 )/( sqrt(h) -1 )`

Evaluate : lim_( x -> 1 ) ( sqrt(x) - 1 + sqrt( x -1 ) )/( sqrt( x^2 -1 ))

Evaluate lim_(hto0) [(1)/(h^(3)sqrt(8+h))-(1)/(2h)].

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

Evaluate the limit: lim_(h rarr0)[(1)/(h root(3)(8+h))-(1)/(2h)]

lim_ (h rarr0) (e ^ (tanh-1)) / (h)

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

Evaluate the following limits: lim_(hto0)((sqrt(1+h)-1)/(h))

Evaluate lim_(hto0)(log_(10)(1+h))/h

(1) If f(x) = sqrt(x) , prove that : (f(x + h) - f(x))/(h) = (1)/(sqrt(x + h) + sqrtx) . (2) If f(x) = x^(2) , find : (f(1.1) - f(1))/(1.1 - 1) .