QUESTION 2 for Gradescope: Determine if the following improp…
QUESTION 2 for Gradescope: Determine if the following improper integrals converge or diverge, or whether it is impossible to tell, based on the information given. Provide a brief explanation of each answer. (Answer all three parts on page 2 of your work.) Part A Information: lim x → ∞ f ( x ) = 0 {“version”:”1.1″,”math”:”\( \lim_{x \to \infty} f(x) =0 \)”} Integral: ∫ 10 ∞ f ( x ) d x {“version”:”1.1″,”math”:”\( \int_{10}^{\infty} f(x) \,dx \)”} Part B Information: lim x → ∞ m ( x ) = 1 7 {“version”:”1.1″,”math”:”\( \lim_{x \to \infty} m(x) = \frac{1}{7} \)”} Integral: ∫ 3 ∞ m ( x ) d x {“version”:”1.1″,”math”:”\( \int_{3}^{\infty} m(x) \,dx \)”} Part C Information: ∫ 5 ∞ f ( x ) d x converges {“version”:”1.1″,”math”:”\( \int_{5}^{\infty} f(x) \,dx \quad \mbox{converges}\)”} Integral: ∫ 5 ∞ ( f ( x ) + 1 ) d x {“version”:”1.1″,”math”:”\( \int_{5}^{\infty} (f(x) + 1) \,dx \)”}