Recent questions tagged goclasses-da-dpp-day-183

For a function $f:[-1,1]\to\mathbb{R}$, consider the following statements:There exists $\epsilon>0$ such that for all $x,y\in(-\epsilon,\epsilon)$, if $x<y$, then $f(x)<f...

Define $F,G:\mathbb{R}\to\mathbb{R}$ by $$F(x)=\int_0^x |t(t-2)|dt \qquad\text{ and }\qquad G(x)=\int_0^x F(t)dt$$ Which of the following is true?$G$ is not differentiabl...

Suppose $f:[0,\infty)\to[0,\infty)$ is continuous, strictly increasing, and onto, and let $g=f^{-1}$. For $a,b>0$, define $$I=\int_0^a f(x)dx+\int_0^b g(y)dy-ab$$ Which o...

Evaluate the limit $L=\lim_{x\to\infty}x\left(\sqrt{x^2+6x+10}-\sqrt{x^2+6x+5}\right)$.$0$ $\dfrac{5}{2}$ $5$ $\infty$

The function $f(x)=3x^5-45x^4+230x^3-450x^2+6x+11$ is concave down on which of the following intervals?$(1,3)\cup(5,\infty)$ $(-\infty,1)\cup(3,5)$ $(-\infty,3)\cup(5,\in...