Question

Ma poate ajuta cineva cu exercitile acestea ?​

Answer 1

Explicație pas cu pas:

a)

$\lim_{x \to 1}( {2}^{ log_{2}(x) } ) = {2}^{ log_{2}(1) } = {2}^{0} = 1$

b)

$\lim_{x \to 0}( {3}^{ log_{3}( {x}^{2} + 1) } ) = {3}^{ log_{3}(0 + 1) } = {3}^{ log_{3}(1) } = {3}^{0} = 1$

c)

$\lim_{x \to 5} log_{5} {2}^{x} = log_{5} {2}^{5} = 5log_{5} 2$

d)

$\lim_{x \to - \infty } log_{3} {\Big( \dfrac{1}{3} \Big)}^{x} = \lim_{x \to - \infty } log_{3} {3}^{ - x} = \\ = \lim_{x \to - \infty } ( - x) = - \lim_{x \to - \infty } x = + \infty$