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Ludmilka [50]
3 years ago
6

Evaluate the following limit.

Mathematics
1 answer:
Rus_ich [418]3 years ago
7 0

Answer:

-191

Step-by-step explanation:

A limit is the value that a function approaches as the input approaches some value.

We say \displaystyle \lim_{x\rightarrow a}f(x)=L if f(x) approaches to L as x approaches to a.

To find:\displaystyle \lim_{x\rightarrow -4}2x^3-4x^2+2x+9

Solution:

Let f(x)=2x^3-4x^2+2x+9

On putting x = -4 in function f(x)=2x^3-4x^2+2x+9, we get

\displaystyle \lim_{x\rightarrow -4}2x^3-4x^2+2x+9\\=2(-4)^3-4(-4)^2+2(-4)+9\\=2(-64)-4(16)-8+9\\=-128-64-8+9\\=-128-63\\=-191

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In the △ABC, the height AN = 24 in, BN = 18 in, AC = 40 in. Find AB and BC. Consider all possible cases. Case 1 : N∈BC, AB = __,
aivan3 [116]

Answer:

Case 1:

AB = 30

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Case 2:

AB = 15.9

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Case 3: Not possible

Step-by-step explanation:

Given

See attachment for illustration of each case

Required

Find AB and BC

Case 1:

Using Pythagoras theorem in ANB, we have:

AB^2 = AN^2 + BN^2

This gives:

AB^2 = 24^2 + 18^2

AB^2 = 576 + 324

AB^2 = 900

Take square roots of both sides

AB = \sqrt{900

AB = 30

To calculate BC, we consider ANC, where:

AC^2 = AN^2 + NC^2

40^2 = 24^2 + NC^2

1600 = 576 + NC^2

Collect like terms

NC^2 = 1600 - 576

NC^2 = 1024

Take square roots

NC = \sqrt{1024

NC = 32

So:

BC = NC + BN

BC = 32 + 18

BC = 50

Case 2:

Using Pythagoras theorem in ANB, we have:

AN^2 = AB^2 + BN^2

This gives:

24^2 = AB^2 + 18^2

576 = AB^2 + 324

Collect like terms

AB^2 = 576 - 324

AB^2 = 252

Take square roots of both sides

AB = \sqrt{252

AB = 15.9

To calculate BC, we consider ABC, where:

AC^2 = AB^2 + BC^2

40^2 = 252 + BC^2

1600 = 252 + BC^2

Collect like terms

BC^2 = 1600 - 252

BC^2 = 1348

Take square roots

BC = \sqrt{1348

BC = 36.7

Case 3:

This is not possible because in ANC

The hypotenuse AN (24) is less than AC (40)

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