Question Type 3: Finding points of intersection of two more difficult functions Exercises

On the domain $x \in [0, 2]$, the curves $y = e^x$ and $e^{y} = 4y + 1$ intersect. Find the intersection point to 3 d.p.

Determine the intersection(s) of $y = 2\cos x$ and $y = e^{-x/2}$ on $x \in [0, 4]$. Give your answers correct to 3 decimal places.

Find all intersections of $y = x e^{-x}$ and $y = 0.1$ for $x \in [0, 10]$. Give answers to 3 d.p.

Find the coordinates of all points of intersection of the curves $y = e^x$ and $y = x + 2$ for $x \in [-3, 2]$. Give your answers correct to 3 decimal places.

Find all points of intersection of the graphs of $y = x^2 - 2$ and $y = 2^x$ for $x \in [-2, 3]$. Give answers correct to 3 d.p.

Find all points where $y = x^3 - x$ intersects $y = 2^x$ on the domain $x \in [-2, 2]$. Give your answers correct to 3 decimal places.

Determine all intersections of $y = \sin x$ and $y = 0.2x$ for $x \in [0, 10]$. Give answers to 3 d.p.

Find the coordinates of all intersection points of the curves $y = e^{-x^2}$ and $y = 0.5$ for $-3 \le x \le 3$. Give the coordinates in exact form and rounded to 3 decimal places.

Find the intersection of $y = \cos x$ and $y = \ln(x+2)$ for $x \in [0, 4]$. Give the point to 3 d.p.

Find all intersection points of $y = |x - 1|$ and $y = \ln(x + 2)$ on $x \in [-1.5, 4]$. Give answers to 3 d.p.

Show that the graphs of $y = \tan x$ and $y = x$ intersect exactly once in the domain $x \in (-1.2, 1.2)$.

Find the intersection point of $y = \ln(x+3)$ and $y = \frac{1}{2}x$ for $x \in [-2, 10]$. Give your answer to 3 d.p.