Continuity of Compositions
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Problems 9
- Is the function f(x)=sin(x)+xcos(x)−e4x2+3f(x) = \sin(x) + x\cos(x) - e^{4x^2 + 3}f(x)=sin(x)+xcos(x)−e4x2+3 continuous for all x∈Rx \in \mathbb{R}x∈R?
- Let fff and ggg be continuous functions. Which of the following is true about function continuity?
- Is h(x)=cos(3x)h(x)=\cos(3x)h(x)=cos(3x) a continuous function?
- On what interval is the function F(x)=ln(x)+13F(x)=\sqrt{\ln(x)+1}^3F(x)=ln(x)+13 continuous?
- Is h(x)=sin(cos(ex)))h(x)=\sin(\cos(e^x)))h(x)=sin(cos(ex))) a continuous function?
- Is h(x)=ln(sin(x))h(x)=\ln(\sin(x))h(x)=ln(sin(x)) a continuous function?
- Is G(x)=3cos((3x−8)−1)G(x)=3^{\cos(\sqrt{(3x-8)^{-1}})}G(x)=3cos((3x−8)−1) a continuous function?
- Is G(x)=esin((3x)2+3(3x)+2)G(x)=e^{\sin((3^x)^2+3(3^x)+2)}G(x)=esin((3x)2+3(3x)+2) a continuous function?
- Is a continuous function on the interval (0,∞)(0,\infty)(0,∞)?