I think it is C. 60.
You can eliminate A because it is not a right angle, and D because the angle is bigger than the given angle. So it is between 50 and 60, and I hope this is right and the picture makes sense

6 0

3 years ago

A. f(x) = 2|2| is differentiable overf X B. g(x) = 2 + || is differentiable over -f

kramer

Recall the definition of absolute value:

• If x ≥ 0, then |x| = x

• If x < 0, then |x| = -x

(a) Splitting up f(x) = x |x| into similar cases, you have

• f(x) = x ² if x ≥ 0

• f(x) = -x ² if x < 0

Differentiating f, you get

• f '(x) = 2x if x > 0 (note the strict inequality now)

• f '(x) = -2x if x < 0

To get the derivative at x = 0, notice that f '(x) approaches 0 from either side, so f '(x) = 0 if x = 0.

The derivative exists on its entire domain, so f(x) is differentiable everywhere, i.e. over the interval (-∞, ∞).

(b) Similarly splitting up g(x) = x + |x| gives

• g(x) = 2x if x ≥ 0

• g(x) = 0 if x < 0

Differentiating gives

• g'(x) = 2 if x > 0

• g'(x) = 0 if x < 0

but this time the limits of g'(x) as x approaches 0 from either side do not match (the limit from the left is 0 while the limit from the right is 2), so g(x) is differentiable everywhere except x = 0, i.e. over the interval (-∞, 0) ∪ (0, ∞).

5 0

3 years ago

What is the shape graphed by the function r = 1+ sin theta

IRISSAK [1]

Answer: Is known as a "heart" shape.

Step-by-step explanation:

r = 1 + sin(θ)

Let's do it without a graph, let's use only math and logic:

remember that θ is measured from the x-axis

when θ = 0, we have r = 1 (so we have a radius of 1 over the x-axis)

when θ = pi/2, we have r = 1 + sin(pi/2) = 2

when θ = pi, we have r = 1 + sin(pi) = 1

when θ = 3*pi/2, we have r = 1 + sin(3*pi/2) = 0

First, we have symetry around the y-axis,

now, notice that the value of x in θ = 0, θ = pi and θ = 3*pi/2 is the same. so this is not a circle, this is actually a circle where the bottom part is flatted.

But not actually flat, because between θ = pi and θ = 2pi we are in the negative y-axis, so in this region we have two small bumps that connect in the point (0, 0)

This is a kinda "heart" shape.

3 0

4 years ago