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shtirl [24]
3 years ago
12

For each of the following functions f(x) below : Find its limits limx→±[infinity]f(x) as x approachs ±[infinity] . Choose the va

lues of x where f(x) is differentiable, i.e. f′(x) exists Choose the values of x where f(x) is also strictly increasing, i.e. f′(x)>0 . For f(x)=max(0,x) : (If the limit diverges to infty, enter inf for [infinity], and -inf for −[infinity] ) limx→−[infinity]f(x)=
Mathematics
1 answer:
kicyunya [14]3 years ago
6 0

Answer:

See below

Step-by-step explanation:

f(x)=\max\{0,x\} then f(x)=0 if x<0 and f(x)=x if x≥0.

When x→-∞, f is the constant function zero, therefore \lim_{n\rightarrow -\infty}f(x)=0. When x→∞, f(x)=x and x grows indefinitely. Thus \lim_{n\rightarrow \infty}f(x)=\infty

f is differentiable if x≠0. If x>0, f'(x)=1 (the derivative of f(x)=x) and if x<0, f'(0)=0 (the derivative of the constant zero). In x=0, the right-hand derivative is 1, but the left-hand derivative is 0, hence f'(0) does not exist,

f'(x)>0 for all x>0. Therefore f(x) is strictly increasing on the inverval (0,∞).

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Translate the figure 5 units up. Then decide if each statement about translated figures is true or false,
m_a_m_a [10]

Answer:

First, second, and third are true.

Fourth is false.

Step-by-step explanation:

1. When we're translating a figure, everything about the figure stays the same except its location on the coordinate plane. The side lengths, the angle measures, and parallel sides will not change.

2. The fourth one is false because two figures/objects are congruent if they have the same shape and size. Since translation only affects the location on a coordinate plane, the original and final figure are congruent.

5 0
3 years ago
3 Ximena draws an X shape in the coordinate plane as shown. Draw the images of
VARVARA [1.3K]

When a shape is rotated, it must be rotated around a point.

<em>See attachment for the image of each rotation.</em>

To do this, the top coordinates of the X shape will be transformed using the appropriate rotation rule; the same rule will then be applied to the other parts of the X shape.

The top coordinates of the X shape are:

A = (0,0)

B = (1,0)

C = (3,0)

D =(4,0)

For 90 degrees counterclockwise rotation, the rule is:

(x,y) \to (-y,x)

So, we have:

A' = (0,0)

B' = (0,1)

C' = (0,3)

D' = (0,4)

For 180 degrees rotation, the rule is:

(x,y) \to (-x,-y)

So, we have:

A' = (0,0)

B' = (-1,0)

C' = (-3,0)

D' = (-4,0)

For 270 degrees counter rotation, the rule is:

(x,y) \to (y,-x)

So, we have:

A' = (0,0)

B' = (0,-1)

C' = (0,-3)

D' = (0,-4)

See attachment for the image of each rotation

Read more about rotations at:

brainly.com/question/1571997

3 0
3 years ago
What is the zscore with a confidence level of 95% when finding the margin of error for the mean of a normally
Inessa [10]

Answer:

Z score with a confidence level of 95% is 1.96

Step-by-step explanation:

The computation of the z score with the confidence level of 95% is shown below:

While determining the margin of error for the normally distributed population from the sample, the z score of the confidence level of 95% is 1.96

The same is to be considered

Therefore the third option is correct

3 0
3 years ago
Read 2 more answers
A cylinder has radius 3 meters. Its volume is 141.3 cubic meters. Find its height to the nearest tenth
Misha Larkins [42]

Answer:

Height = 5meters

Step-by-step explanation:

Using the formula h= v over 3.14r^2 = 141.3 over 3.14 times 3^2 gives us 4.99747 meters.

3 0
3 years ago
Which number is a multiple of 7? A 27 B 48 C 56 ET D 74​
saul85 [17]

Answer:

C. 56

Step-by-step explanation:

7*8=56

7 0
3 years ago
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