Linear Algebra
The table below shows number of responses on whether 8th grade students enjoy using Canvas.
What percent of the students who do NOT enjoy using Canvas is a girl? Round your answer to the nearest tenth.
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Linear Algebra
\text { 4] Find } g(0)-g(9)+g(2) \text {, if }
g(x)=\left\{\begin{aligned}
\frac{x+1}{2}, & \text { if } x \text { is odd } \\
\frac{x}{2}, & \text { if } x \text { is even }
\end{aligned}\right.
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Linear Algebra
\text { 3] Find } f(4)-f(2)+f(3) \text {, if }
f(x)=\left\{\begin{array}{ll}
\frac{x+1}{2}, & \text { if } x \text { is odd } \\
\frac{x}{4}, & \text { if } x \text { is even }
\end{array}\right.
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Linear Algebra
2] Find the Domains of the following functions:
\text { a) } f(x)=\sqrt{15-5 x}
f(x)=\frac{x^{2}-2 x+1}{x^{2}-4 x-21}
f(x)=\frac{x^{2}-2 x+1}{\sqrt{16-2 x}}
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Linear Algebra
a) Give the definition of a rational function. [5 pts]
b) Give an example of a polynomial function of degree 3. [5 pts]
c) Can a constant function be a polynomial and a rational function at the same time? Explain your answer. [5 pts]
d) Give an example of a non-polynomial function and explain why not apolynomial function. [10 pts)
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Linear Algebra
5) Ве,
\begin{array}{c}
f: \mathbb{R} \rightarrow \mathbb{R} \\
f(x)=\left\{\begin{array}{ll}
x^{2}-3 \cos (\pi x) & x<0 \\
x-4 e^{-2 x} & x \geq 0 .
\end{array}\right.
\end{array}
Calculate
\int_{-1}^{2} f(x) d x
Presenting the result in simplified form
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Linear Algebra
4) Be f: R - Ra function differentiable in R such your derivative f', has in maximum a real zero.
Prove that the equation f(x)=0 has in maximum 2 real square
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Linear Algebra
3) Take in consideration the following function
f(x)=\left\{\begin{array}{ll}
f: \mathbb{R} \rightarrow \mathbb{R} & \\
\frac{x^{2}-4 x+\cos (\sin (x)),}{x^{4}+4 x^{2}+1}, & x \leq 0
\end{array}\right.
a) Show that the function f is continuous in R+ and in R- but discontinuous in the point X
b) Say justifying, if f is differenciable in X=0
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Linear Algebra
2) Prove by definition that
\lim _{x \rightarrow 0} x^{2} \cos \left(e^{x}\right)=0
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Linear Algebra
1) Calculate the following limit:
\lim _{x \rightarrow+\infty} \frac{x^{2}\left(e^{-3 x}+1\right)+x \cos (5 x)}{x^{2}+7 x+1}
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Linear Algebra
7. Consider the following problem.
Maximize Z = 6X1 + 8X2
5X1 + 2X2 <=20
X1 + 2X2 <=10
X1, X2 >= 0
a. Construct the dual problem for this primal problem
b. Solve both the primal problem and the dual problem graphically.Identify the CPF (Corner-Point Feasible) solutions and corner -pointinfeasible solutions for both problems. Calculate the objectivefunction values for all these solutions.
c. Construct a table listing the complementary basic solutions for theseproblems.
d. Work through the simplex method step by step to solve the primal problem. After each iteration, identify the basic feasible (BF) solution for this problem and the complementary basic solution for the dual problem. Also identify the corresponding corner-point solutions.
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