Sketch a graph of the plane and label any intercepts. 2x - y + 3z = 4

The celebrated example due to Karl Weierstrass of a nowhere differentiable continuous function $f(x)$ in $-\infty<x<\infty$ is given by

$$f(x)=\sum_{n=0}^{\infty}\left(\frac{3}{4}\right)^n \phi\left(4^n x\right),$$

where $\phi(x+2)=\phi(x)$, and $\phi(x)$ on $0 \leqslant x \leqslant 2$ is the "triangle" through $(0,0),(1,1),(2,0)$. By construction, $0 \leqslant \phi\left(4^n x\right) \leqslant 1$. Verify by means of the comparison test that the series converges for any value of $x$. [See Counterexamples in Analysis by B. R. Gelbaum and J. M. H. Olmsted, HoldenDay, San Francisco (1964), p. 38 for the proof that $f$ is nowhere differentiable.]

Describe what the formula $x=f^{-1}(y)$ tells you in practical terms.

Solve each pure-time differential equation. $\frac{d y}{d x}=e^{-3 x}, \text { where } y_{0}=10 \text { for } x_{0}=0$

Are there any points in the coordinate plane that are not solutions of either y > x - 2 or y < x - 2? Explain.

Draw a coordinate plane. Then graph each point.

$$C(2, 5)$$

delete

Tiffany makes scarves and sells them at a neighborhood clothing store. The owner charges her $25 a day for the space she uses. She sells each scarf for$30. Each scarf costs her $14 to make. How many scarves must Tiffany sell per day to make a profit of at least$100 per day? Write and solve an inequality. Show your work.

The z-plane region D consists of the complex numbers z = x + y i that satisfy the given conditions. Describe (or sketch) the image R of D in the w-plane under the given function $q=f(z)$. $0<x<\frac{\pi}{2}, 0<y<\infty: \quad w=e^{iz}$.

Use an augmented matrix to solve the system of equations. x - 2y = -15, 2x + 5y = 78

The cortical regions that are NOT directly involved in sensory or motor functions are known as:

A. the limbic system

B. frontal lobes

C. association areas

D. parietal lobes

The graph of $f$ is shown. Evaluate $\int_0^5 f(x)~dx$ by interpreting it in terms of areas.

Write an augmented matrix for the system of equations.

$$-3 x+4 y=22$$

$$2 x-3 y=6$$

Assume the declarations of Exercise 10. Write C++ statements that update the gpa of the 10th student in the array classList by adding 0.75 to its previous value.