Question Type 4: Solving using graph function Exercises

Determine all solutions of $e^x = \sin x$ in the interval $[-10, 0]$ using a graphing calculator. List each solution to two decimal places.

Find the first two negative solutions of the equation $e^x=\sin x$ using the graphing calculator's intersection feature. Give each solution to three decimal places.

How many real solutions does the equation $e^x=\sin x$ have? Explain your answer using a sketch or graph of the two functions.

Use graphical reasoning to explain why there are infinitely many negative solutions to the equation $e^x=\sin x$.

Use a graphing calculator to solve $e^x=\sin x$ for the unique solution in the interval $[-4,-3]$. Give your answer to three decimal places.

Plot the function $f(x)=e^x-\sin x$ on a graphing calculator and use it to determine an interval of length $0.5$ that contains the root nearest to $x=-3$. Then refine this root to four decimal places using the intersection feature.

Use a sketch of the graphs of $y=e^x$ and $y=\sin x$ to explain why the equation $e^x=\sin x$ has no solutions for $x>0$.

Estimate all solutions of $e^x=\sin x$ in the interval $[-2\pi,0]$ by plotting the functions on a graphing calculator. List each solution to two decimal places.

Find the x-coordinate of the intersection of $y=e^x$ and $y=\sin x$ nearest to $x=-9$. Give your answer to three decimal places using a graphing calculator.

Sketch $y=e^x$ and $y=\sin x$ for $x$ from $-8$ to $-2$ and estimate the number of intersections. Use a graphing calculator to confirm the number and list their approximate $x$-coordinates to one decimal place.

Use a graphing calculator to plot the functions $y=e^x$ and $y=\sin x$ on the interval $[-4,-3]$. Estimate the $x$-coordinate of their intersection to two decimal places.