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.