IB Mathematics Analysis and Approaches Question Type 3: Using Calculator to Graph Equations and Find Solutions to Inequalities Exercises

Using a graphing calculator, solve on the interval $0\le x\le 2\pi$: $\sin x>0.3$. Give your answer as interval(s) with endpoints to 3 d.p.

Using a graphing calculator, solve the inequality $e^x<2-x$ on $\mathbb{R}$, giving the boundary value to 3 significant figures.

Use a graphing calculator to solve for $x$ in $[0,3]$: $\cos x=\ln (x+2)$. Give the solution to 3 d.p.

Using a graphing calculator, solve $e^x\ge 3x$ on $\mathbb{R}$. Give the boundary values to 3 d.p.

Using a graphing calculator, solve $e^{-x^2}\ge 0.2$ on $\mathbb{R}$. Give endpoints to 3 d.p.

Using a graphing calculator, solve for $x>0$: $\ln x\le 1-\frac{x}{2}$. Give the boundary value to 3 d.p.

By sketching a suitable graph, solve $\ln (x+1)>2-x$ for $x>-1$. Give the critical value to 3 decimal places.

Using a graphing calculator, solve $\cos x\ge 0.2x$ on $[-2,2]$. Give endpoints to 3 d.p.

Using a graphing calculator, solve $|x|\le e^{-x}$ on $\mathbb{R}$. Give the positive boundary to 3 d.p.

Using a graphing calculator, solve $2^x\le x^2+1$ on $\mathbb{R}$. Give the largest boundary value to 3 d.p.

Using a graphing calculator, solve on $\left(-\frac{\pi }{3},\frac{\pi }{3}\right)$: $\tan x\ge x$.

Using a graphing calculator, solve $\sin x<\frac{x}{5}$ on $[-\pi ,\pi ]$. Give numerical endpoints to 3 d.p.