When it comes to finding the value of a variable, the process usually involves making sure the variable is alone on one side of an equation. This may necessitate the use of various mathematical techniques such as multiplication, division, addition, or subtraction. The ultimate aim is to identify the exact value that will validate the equation when it replaces the variable.
| Topic | Problem | Solution |
|---|---|---|
| None | Let $f(x, y)=2^{x}+9 x y$, find $f(0,-3), f(-3,2)… | Given the function \(f(x, y)=2^{x}+9 x y\), we are asked to find the values of \(f(0,-3)\), \(f(-3,… |
| None | Find and simplify the difference quotient $\frac{… | We are given the function \(f(x) = -5x\). |
| None | Given $f(x)=4 x-2$ (a) Find $f(x+h)$ and simplify… | Substitute \(x+h\) into the function \(f(x) = 4x - 2\) to get \(f(x+h) = 4(x+h) - 2\) |
| None | Find numbers $k$, so that $f$ is continuous at ev… | For a function to be continuous at a point, the limit of the function as x approaches that point fr… |
| None | 1. Simplify $\frac{\left(x^{3}+x\right) \sinh \le… | Rewrite the expression using natural logarithm notation (ln) instead of log base e: \(\frac{\left(x… |
| None | Find the difference quotient of $f$; that is, fin… | Given the function \(f(x)=8x+7\) |
| None | Find and simplify the difference quotient $\frac{… | Substitute \(x+h\) into the function to get \(f(x+h) = 5(x+h)^2\). |
| None | Write the given expression as a single quotient i… | Given the expression \(2x(x^{2}+1)^{1 / 2}+x^{2} \cdot \frac{1}{2}(x^{2}+1)^{-1 / 2} \cdot 2x\) |
| None | Find the difference quotient and simplify your an… | f(x)=x^2-2x+4 \Rightarrow f(6)=6^2-2(6)+4 |
| None | A particle moves according to the equation \( x=5… | \(x = 5t^5 + 2\) |
| None | Find the difference quotient $\frac{f(x+h)-f(x)}{… | The difference quotient is a measure of the average rate of change of the function over the interva… |