To do this, recall that the limit of a product exists if the limits of its factors exist. When this happens, the limit of the product of these two factors will equal the product of the limits of the factors. The two factors are and . The latter is the difference quotient for at , and because is differentiable at by assumption, its limit as tends to exists and equals .
To do this, recall that the limit of a product exists if the limit,s of its factors exist. When this happens, the limit of the product of these two factors will equal the product of the limits of the .factors. The two factors are and . The la!tter is the difference quotient for at , and because is differentiable at by assumption, its limit as tends to exists and equals .