Continuity of Products and Quotients
Read this topicExplanations 1
Problems 8
- Let fff and ggg be continuous functions. Which of the following is true about function continuity?
- Let f(x)=x2+2x−1f(x)=x^2+2x-1f(x)=x2+2x−1 and g(x)=3xg(x)=3xg(x)=3x. Is f(x)∗g(x)f(x)*g(x)f(x)∗g(x) continuous?
- Let f(x)=x2+2x−15f(x)=x^2+2x-15f(x)=x2+2x−15 and g(x)=x+5g(x)=x+5g(x)=x+5. Is f(x)g(x)\frac{f(x)}{g(x)}g(x)f(x) continuous?
- Let f(x)=x−2f(x)=x-2f(x)=x−2 and g(x)=x2−5x+8g(x)=x^2-5x+8g(x)=x2−5x+8. Is f(x)g(x)\frac{f(x)}{g(x)}g(x)f(x) continuous?
- Let f(x)=x2+3x+2f(x)=x^2+3x+2f(x)=x2+3x+2 and g(x)=x2−ax+3g(x)=x^2-ax+3g(x)=x2−ax+3. What value of aaa will make f(x)g(x)\frac{f(x)}{g(x)}g(x)f(x) continuous?
- Let f(x)=exf(x)=e^xf(x)=ex and g(x)=ln(x)g(x)=\ln(x)g(x)=ln(x). Is f(x)g(x)\frac{f(x)}{g(x)}g(x)f(x) continuous?
- Let f(x)=exf(x)=e^xf(x)=ex and g(x)=ln(x)g(x)=\ln(x)g(x)=ln(x). Is g(x)f(x)\frac{g(x)}{f(x)}f(x)g(x) continuous?
- Let f(x)=xf(x)=\sqrt{x}f(x)=x and g(x)=axg(x)=a^xg(x)=ax. For which values of aaa is f(x)g(x)\frac{f(x)}{g(x)}g(x)f(x) continuous?