In Exercises 25 through 30, find the matrix B of the linear transformation with respect to the basis

L'Hospital's Rule Find lim(ln(x) x−1 x→0 As x→1, ln(x)→0 and (x-1) → 0 This is called an indeterminate form of type 0/0 Now consider lim (ln(x)) x−1 x→ ∞ As x→ ∞ ln(x)→ ∞ nd (x-1) →∞ ndeterminate form of type∞ / ∞ L'Hospital's rule If f(x) and g(x) are both differentiable and / 0a) = suppose that lim(f(x)) = 0 and lim(g(x)) = 0 x→a x→a Or that lim(f(x))∞= nd lim(g(x)) ∞ x→a x→a f(x) f′(x) Then lim (g(x) ) lim(g′x)) x→a x→a Note: This is not the quotient rule take f’(x) and g’(x) separately Ex. Find lim(ln(x)/(x-1)) = lim((1/x)/1) = lim(x/1) = 1/1 = 1 x→1 x→1 x→1 Ex. Find lim(ln(x)/(x-1)) = lim(1/x) = 0 x→