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3 years ago

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Mathematics

1 answer:

Dafna1 [17]3 years ago

5 0

1/5 since there’s 5 possibilities and one green

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Determine the values of the constants b and c so that the function given below is differentiable. f(x)={2xbx2+cxx≤1x>1

Lera25 [3.4K]

Assuming the function is

$f(x)=\begin{cases}2x&\text{for }x\le1\\bx^2+cx&\text{for }x>1\end{cases}$

For $f(x)$ to be differentiable, it necessarily has to be continuous. For this condition to be met, we need

$\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1^+}f(x)=f(1)$
$\iff\displaystyle\lim_{x\to1}2x=\lim_{x\to1}(bx^2+cx)$
$\iff2=b+c$

For the derivative to exist, the one-sided limits of the derivative must also exist and be equal. We have

$f'(x)=\begin{cases}2&\text{for }x1\end{cases}$

$\displaystyle\lim_{x\to1^-}2=\lim_{x\to1^+}(2bx+c)$
$\iff2=2b+c$

Now we solve for $b$ and $c$ :

$\begin{cases}b+c=2\\2b+c=2\end{cases}\implies b=0,c=2$

5 0

3 years ago

If f(x)=2x+5, then what is f(3)?

FromTheMoon [43]

Answer:

$\Large \boxed{f(3)=11}$

Step-by-step explanation:

$f(x)=2x+5$

For f(3), the input for the function f(x) is 3.

Let x (input) = 3.

$f(3)=2(3)+5 \\\\ f(3)=6+5 \\\\ f(3)=11$

7 0

3 years ago

Read 2 more answers

Use the Distance Formula to find the distance between D(2, 0) and E(8, 6).

Mazyrski [523]

Answer:

The answer is

<h2> $6 \sqrt{2} \: \: \: or \: \: \: 8.50 \: \: \: \: units$ </h2>

Step-by-step explanation:

The distance between two points can be found by using the formula

$d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\$

where

(x1 , y1) and (x2 , y2) are the points

From the question

The points are D(2, 0) and E(8, 6

The distance between them is

$|DE| = \sqrt{ ({2 - 8})^{2} + ({0 - 6})^{2} } \\ = \sqrt{( { - 6})^{2} + ( { - 6})^{2} } \\ = \sqrt{36 + 36} \\ = \sqrt{72} \: \: \: \: \: \: \: \: \: \: \\ = 6 \sqrt{2} \: \: \: \: \: \: \: \: \: \: \\ = 8.4852813$

We have the final answer as

$6 \sqrt{2} \: \: \: or \: \: \: 8.50 \: \: \: \: units$

Hope this helps you

5 0

3 years ago

A ball falls from a window. Its height, as a function of time, is modeled by y=-4.9x2 + 12. Which statement best describes the f

ankoles [38]

Answer:The function is nonlinear

Step-by-step explanation:

Took the test made a 100

5 0

3 years ago

Read 2 more answers

HELP<br> What is the volume of the cylinder below ?

blagie [28]

Answer:

C. 2448π units³

Step-by-step explanation:

V = π·r²·h

= π·12²×17

= 144×17·π

= 2448π units³

7 0

3 years ago

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