1+10=10 2+20 =20 3+30=28 4+40=32 5+50=28 6+60=?

The graph of f is given. State the numbers at which f is not differentiable.

Andreas93 [3]

Answer:

When we have a function f(x), the values of x at which the function is not differentiable are:

1) values at which the function is not "soft". So if we have a really abrupt change in the curvature of the function, we can not differentiate in that value of x, because in those abrupt changes there are a lot of tangent lines to them.

One example of this is the peak we can see at x = -4

Then we can not differentiate the function at x = -4

2) When we have a discontinuity.

If we have a discontinuity at x = x0, then we will have two possible tangents at x = x0, this means taht we can not differentiate at x = x0, and remember that a discontinuity at x = x0 means that:

f(x0₊) ≠ f(x0₋)

where x0₊ is a value that approaches x0 from above, and x0₋ is a value that approaches x0 from below.

With this in mind, we can see in the graph a discontinuity at x = 0, so we can not differentiate the function at x = 0.

4 0

3 years ago

T 3.7.4 Quiz: Working With the Di

koban [17]

Answer:

A

Step-by-step explanation:

3 0

3 years ago

Q7 Q16.) Convert the polar equation to a rectangular equation.

Mekhanik [1.2K]

In polar coordinates, we have

$x=r\cos\theta\implies\cos\theta=\dfrac xr$
$y=r\sin\theta\implies\sin\theta=\dfrac yr$

From this we can write

$\tan\theta=\dfrac{\sin\theta}{\cos\theta}=\dfrac{\frac yr}{\frac xr}=\dfrac yx$

If $\theta=\dfrac{4\pi}3$ , then $\tan\theta=\sqrt$ , so we get

$\dfrac yx=\sqrt3\implies y=\sqrt3\,x$

4 0

3 years ago

Solve the system of equation 0.4x – 3y = 7 3x + 14y = 10 using Cramer's Rule.

Makovka662 [10]

Answer:

for 0.4x – 3y = 7

Step-by-step explanation:

The answer is Changes made to your input should not affect the solution:

(1): "0.4" was replaced by "(4/10)".

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

(4/10)*x-3*y-(7)=0

STEP

1

:

2

Simplify —

5

Equation at the end of step

1

:

2

((— • x) - 3y) - 7 = 0

5

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 5 as the denominator :

3y 3y • 5

3y = —— = ——————

1 5

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

2x - (3y • 5) 2x - 15y

————————————— = ————————

5 5

Equation at the end of step

2

:

(2x - 15y)

—————————— - 7 = 0

5

STEP

3

:

Rewriting the whole as an Equivalent Fraction :

3.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 5 as the denominator :

7 7 • 5

7 = — = —————

1 5

Adding fractions that have a common denominator :

3.2 Adding up the two equivalent fractions

(2x-15y) - (7 • 5) 2x - 15y - 35

—————————————————— = —————————————

5 5

Equation at the end of step

3

:

2x - 15y - 35

————————————— = 0

5

STEP

4

:

When a fraction equals zero :

4.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

2x-15y-35

————————— • 5 = 0 • 5

5

Now, on the left hand side, the 5 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

2x-15y-35 = 0

Equation of a Straight Line

4.2 Solve 2x-15y-35 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 2x-15y-35 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 7/-3 so this line "cuts" the y axis at y=-2.33333

y-intercept = 35/-15 = 7/-3 = -2.33333

Calculate the X-Intercept :

When y = 0 the value of x is 35/2 Our line therefore "cuts" the x axis at x=17.50000

x-intercept = 35/2 = 17.50000

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -2.333 and for x=2.000, the value of y is -2.067. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -2.067 - (-2.333) = 0.267 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = 0.267/2.000 = 0.133

Geometric figure: Straight Line

Slope = 0.267/2.000 = 0.133

x-intercept = 35/2 = 17.50000

y-intercept = 35/-15 = 7/-3 = -2.33333

6 0

3 years ago

Which of the following is equal to the expression x+4x/x^2-2x?

noname [10]

Which of the following expression is equal to the following expression:
X + 4x / X^2 - 2x
= 5/X-2

3 0

3 years ago