OMG PLZ HELP I NEED THIS NOW!!

Katen [24]

Uhhh juJjJiaiaiaiaus

8 0

3 years ago

Evaluate the function at the given numbers( correct to six decimal places). Use the results to guess the value of the limit or e

netineya [11]

Answer:

Value of the limit is 0.5.

Step-by-step explanation:

Given,

$F(x)=\frac{e^x-1-x}{x^2}$

When,

$x=1,F(1)=frac{e^1-1-1}{1}=e-2=0.718281$

$x=0.5, F(0.5)=\frac{e^0.5-1-0.5}{(0.5)^2}=0.594885$

$x=0.1, F(0.1)=\frac{e^0.1-1-0.1}{(0.1)^2}=0.517091$

$x=0.05, F(0.05)=\frac{e^0.05-1-0.05}{(0.05)^2}=0.508438$

$x=0.01, F(0.01)=\frac{e^0.01-1-0.01}{(0.01)^2}=0.501670 \hfill (1)$

Correct upto six decimal places.

Now,

$\lim_{x\to 0}F(x)=\lim_{x\to 0}\frac{e^x-1-x}{x^2}$ $(\frac{0}{0})$ form, applying L-Hospital rule that is differentiating numerator and denominator we get,

$\lim_{x\to 0}F(x)$

$=\lim_{x\to 0}\frac{e^x-1}{2x}$ $(\frac{0}{0})$ form.

$=\lim_{x\to 0}\frac{e^x}{2}=\frac{1}{2}=0.5\hfill (2)$

Limit exist and is 0.5. That is according to (1) we can see as the value of x lesser than 1 and tending to near 0, value of the function decreases respectively. And from (2) it shows ultimately it decreases and reach at 0.5, consider as limit point of F(x).

8 0

3 years ago

<img src="https://tex.z-dn.net/?f=%20%5Cboxed%7B%5Cboxed%7B%20%5Cbegin%7Barray%7D%7B%7D%5Clarge%5Ctt%20The%20%20%5C%5C%20%20%5Ct

larisa86 [58]

Distance formula

$\boxed{\sf \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}$

Now

#1

$\\ \tt\Rrightarrow AB=\sqrt{(3-3)^2+(-2-8)^2}=\sqrt{100}=10units$

#2

$\\ \tt\Rrightarrow OK=\sqrt{(5-7)^2+(-2+2)^2}=\sqrt{4}=2units$

#3

$\\ \tt\Rrightarrow LM=\sqrt{(-4-4)^2+(6+4)^2}=\sqrt{64+100}=\sqrt{164}\approx 13units$

#4

$\\ \tt\Rrightarrow PC=\sqrt{(5-2)^2+(1-3)^2}=\sqrt{9+4}=\sqrt{13}=3.2units$

#5

$\\ \tt\Rrightarrow QR=\sqrt{(-2+10)^2+(3-9)^2}=\sqrt{64+36}=\sqrt{100}=10units$

8 0

2 years ago

Read 2 more answers

f the length of side a is 12 centimeters, m= 36°, and m= 75°, what is the length of side b? Round your response to two decimal p

-Dominant- [34]

Answer:

Option C. is correct

Step-by-step explanation:

In the triangle ABC, vertices are A(12, 8), B(4, 8) and C(4, 14)

AB =

BC =

AC =

In triangle XYZ vertices are X(6,6), Y(4,12) and Z(10, 14)

XY =

YZ =

XZ =

In triangle MNO, vertices are M(4, 16), N(4, 8) and O(-2, 8)

MN =

MO =

NO =

In triangle JKL, vertices are J(14, -2), K(12,2) and L(20, 4)

JK =

KL =

JL =

Now we compare the sides for the congruence

Since AB = MN = 8

BC = NO = 6

AC = OM = 10

So ΔABC ≅ Δ MNO

Option C. is correct

Read more on Brainly.com - brainly.com/question/1747695#readmore

3 0

3 years ago

if the area of a rectangle is expressed as x^4 - 9y^2, then the product of the length and the width of the rectangle could be ex

kvasek [131]

Answer:the product of the length and the width of the rectangle could be expressed as

(x^2 - 3y)(x^2 + 3y)

Step-by-step explanation:

If the area of a rectangle is expressed as x^4 - 9y^2, we would determine the dimensions by simplifying the given expression. The simplified expression becomes

(x^2 - 3y)(x^2 + 3y)

Let us check by multiplying each term in one parenthesis by each term in the other parenthesis to get the given expression. It becomes

(x^2 - 3y)(x^2 + 3y) = x^4 + 3x^2y - 3x^2y - 9y^2 = x^4 - 9y^2

6 0

3 years ago