Decide whether the function is continuous on the given interval. If not, define or redefine the function at one point to make it continuous everywhere on the given interval, or else explain why that cannot be done.

$$f(x)=\frac{x+4}{x-8} \text { on }[0,10]$$

For the following exercise, determine the point(s), if any, at which the function is discontinuous. Classify any discontinuity as jump, removable, infinite, or other. $f(x)=\frac{5}{e^{x}-2}$

For the following exercise, determine the point(s), if any, at which the function is discontinuous. Classify any discontinuity as jump, removable, infinite, or other. $f(x)=\frac{x}{x^{2}-x}$

In the following exercise, use the graph of the function y = f(x) shown here to find the values, if possible. Estimate when necessary. $\lim _{x \rightarrow 0^{-}} f(x)$

Sketch the graph of the given function by making a table of values. (Use a calculator if necessary.) $g ( x ) = \left( \frac { 3 } { 2 } \right) ^ { - x }$

Find all points at which the two curves intersect. $r=1+\sin \theta$ and $r=1+\cos \theta$

In the following exercise, use direct substitution to show that the limit leads to the indeterminate form 0/0. Then, evaluate the limit. $\lim _{x \rightarrow 2} \frac{x-2}{x^{2}-2 x}$

For the following exercise, consider the function $f(x)=-x^{2}+1$. Approximate the area of the region between the x-axis and the graph of f over the interval [-1, 1].

For the following exercise, consider the function $f(x)=-x^{2}+1$. Sketch the graph of f over the interval [-1, 1].

Which statements are true about electronegativity? (a) Electronegativity increases from left to right in a period of the Periodic Table. (b) Electronegativity increases from top to bottom in a column of the Periodic Table. (c) Hydrogen, the element with the lowest atomic number, has the smallest electronegativity. (d) The higher the atomic number of an element, the greater its electronegativity.

For the following exercise, points P(4, 2) and Q(x, y) are on the graph of the function $f(x)=\sqrt{x}$. Use the value in the preceding exercise to find the equation of the tangent line at point P.

Calculate the determinant of each of the following matrices: *(a)

$$\left[ \begin{array}{rrrr}{5} & {2} & {1} & {0} \\ {-1} & {3} & {5} & {2} \\ {4} & {1} & {0} & {2} \\ {0} & {2} & {3} & {0}\end{array}\right]$$

, (b)

$$\left[ \begin{array}{rrrr}{0} & {5} & {4} & {0} \\ {4} & {1} & {-2} & {7} \\ {-1} & {0} & {3} & {0} \\ {0} & {2} & {1} & {5}\end{array}\right]$$

, (c)

$$\left[ \begin{array}{rrrr}{2} & {1} & {9} & {7} \\ {0} & {-1} & {3} & {8} \\ {0} & {0} & {5} & {2} \\ {0} & {0} & {0} & {6}\end{array}\right]$$

, *(d)

$$\left[ \begin{array}{rrrrr}{0} & {4} & {1} & {3} & {-2} \\ {2} & {2} & {3} & {-1} & {0} \\ {3} & {1} & {2} & {-5} & {1} \\ {1} & {0} & {-4} & {0} & {0} \\ {0} & {3} & {0} & {0} & {2}\end{array}\right]$$

.

Find the zeros of each function. $f(x)=(x-11)(x-1)$ _____.

If $g : B 7 \rightarrow B$ is a Boolean function of the Boolean variables x1, x2, ..., x7, how many 1’s are needed in the Karnaugh map of gin order to represent the product term (a) x1; (b) x1x2; (C) $x_{1} \overline{x}_{2} x_{3};$ (d) x1x3x5x7?