Property 3
Limit of Exponential Functions
\(f(x)=a^{g(x)}\qquad a>0\qquad a\ne1\)
Exponential function is defined and continuous in all real numbers. Accordingly limit on a point is equal to the image on the same point.
\(f(x)=a^x\quad a>1\)
\(1<a\)
\(a^\infty=\infty\)
\(a^{-\infty}=0\)
\(f(x)=a^x\quad0<a<1\)
\(0<a<1\)
\(a^\infty=0\)
\(a^{-\infty}=\infty\)
1.
\(\lim\limits_{x\to2}(3^x+1)=?\)
2.
\(\lim\limits_{x\to-1}(4^x-1)=?\)
3.
\(\lim\limits_{x\to1}(2^x+x^2-2)=?\)
4.
\(\lim\limits_{x\to\infty}(4^x-3)=?\)
5.
\(\lim\limits_{x\to0}\left(\samefrac{3^x+3^x}{5^x}\right)=?\)
6.
\(\lim\limits_{x\to-\infty}(2^x-7)=?\)
7.
\(\lim\limits_{x\to\infty}\left(\samefrac35\right)^x=?\)
8.
\(\lim\limits_{x\to-\infty}\left(\samefrac74\right)^x=?\)
9.
\(\lim\limits_{x\to-\infty}(9^x+1)=?\)
10.
\(\lim\limits_{x\to-\infty}\left(3^{\samefrac1x}\right)=?\)
11.
\(\lim\limits_{x\to0^-}\left(3^x+3^{\samefrac1x}\right)=?\)