1.

`lim_(x->0) (sinx-sina)/(sqrt(x)-sqrt(a))`

Answer» `sinx-sina = 2sin((x-a)/2)cos((x+a)/2)`
`1/(sqrtx -sqrta) = 1/(sqrtx -sqrta)**(sqrtx +sqrta)/(sqrtx + sqrta) `
`= (sqrtx + sqrta)/(x-a)`
Putting these values in the given expression,
`Lim_(x->a) (2sin((x-a)/2)cos((x+a)/2))/((sqrtx + sqrta)/(x-a))`
`=2 Lim_(x->a) ( (sin((x-a)/2))/(2((x-a)/2))**cos((x+a)/2)**(sqrtx + sqrta))`
`= 2/2 Lim_(x->a) ( (sin((x-a)/2))/(((x-a)/2))) Lim_(x->a)cos((x+a)/2)**(sqrtx + sqrta)`
Applying limits,
`=1*cosa*2sqrta`
`=2sqrtacosa`, which is the required value.


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