Explanation is given below

Question

asked 2021-06-09

\(f(x) =1 − x^2 \text{ if } x \leq 1\)

\(\ln(x) \text{ if } x > 1\)

asked 2021-08-05

Exponentials of an Arithmetic Sequence, If \(\displaystyle{a}_{{{1}}},{a}_{{{2}}},{a}_{{{3}}},\cdots\) is an arithmetic sequence with common difference d, show that the sequence \(\displaystyle{10}^{{{a}_{{{1}}}}},{10}^{{{a}_{{{2}}}}},{10}^{{{a}_{{{3}}}}},\cdots\) is a geometric sequence, and find the common ratio.

asked 2021-08-03

Determine whether \(\displaystyle{g{{\left({x}\right)}}}={x}^{{\frac{{3}}{{2}}}}−{x}^{{{2}}}+{2}\) is a polynomial. If it is, state its degree. If not, say why it is not a polynomial. If it is a polynomial, write it in standard form. Identify the leading term and the constant term.

asked 2021-08-03

Determine whether \(\displaystyle{g{{\left({x}\right)}}}=\frac{{x}^{{{3}}}}{{2}}−{x}^{{{2}}}+{2}\) is a polynomial. If it is, state its degree. If not, say why it is not a polynomial. If it is a polynomial, write it in standard form. Identify the leading term and the constant term.