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hammer [34]
3 years ago
12

Lim x--> 0 (e^x(sinx)(tax))/x^2

Mathematics
1 answer:
Tom [10]3 years ago
4 0

Make use of the known limit,

\displaystyle\lim_{x\to0}\frac{\sin x}x=1

We have

\displaystyle\lim_{x\to0}\frac{e^x\sin x\tan x}{x^2}=\left(\lim_{x\to0}\frac{e^x}{\cos x}\right)\left(\lim_{x\to0}\frac{\sin^2x}{x^2}\right)

since \tan x=\dfrac{\sin x}{\cos x}, and the limit of a product is the same as the product of limits.

\dfrac{e^x}{\cos x} is continuous at x=0, and \dfrac{e^0}{\cos 0}=1. The remaining limit is also 1, since

\displaystyle\lim_{x\to0}\frac{\sin^2x}{x^2}=\left(\lim_{x\to0}\frac{\sin x}x\right)^2=1^2=1

so the overall limit is 1.

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81 Bags of Shells

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Anyone know the correct answer to this?
Svetllana [295]

Answer:

It should be y=4x-7

Step-by-step explanation:

M is the slope meaning Δx over Δy or rise over run

So if you look at (2,2) and count up to (3,6) the rise is 4 and the run is 1 meaning the slope is 4.

B is the y- intercept so then it would just be -7.

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the height in feet above the ground of an arrow after it is shot can be modeled by y=-16r^2+63r+4.Can the arrow pass over a tree
miss Akunina [59]

Answer:

yes

Step-by-step explanation:

y=-16r^2+63r+4

maximum value of y :

y'=0

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= -4 + 124 + 4 = 124 ft

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7 0
3 years ago
The sample space of a random experiment is {a, b, c, d, e} with probabilities 0.1, 0.1, 0.2, 0.4, and 0.2 respectively. Let A de
antoniya [11.8K]

Answer:

a) P(A) =P(a)+P(b) +P(c)= 0.1+0.1+0.2 = 0.4

b) P(B) =P(c) +P(d)+P(e)=0.2+0.4+0.2=0.8

c) P(A') = 1-P(A) =1-0.4=0.6

d) P(A \cup B) =0.4 +0.8-0.2 =1.0

e)  The intersection between the set A and B is the element c so then we have this:

P(A \cap B) = P(c) =0.2

Step-by-step explanation:

We have the following space provided:

S= [a,b,c,d,e]

With the following probabilities:

P(a) =0.1, P(b)=0.1, P(c) =0.2, P(d)=0.4, P(e)=0.2

And we define the following events:

A= [a,b,c], B=[c,d,e]

For this case we can find the individual probabilities for A and B like this:

P(A) = 0.1+0.1+0.2 = 0.4

P(B) =0.2+0.4+0.2=0.8

Determine:

a. P(A)

P(A) =P(a)+P(b) +P(c)= 0.1+0.1+0.2 = 0.4

b. P(B)

P(B) =P(c) +P(d)+P(e)=0.2+0.4+0.2=0.8

c. P(A’)

From definition of complement we have this:

P(A') = 1-P(A) =1-0.4=0.6

d. P(AUB)

Using the total law of probability we got:

P(A \cup B) =P(A) +P(B)-P(A \cap B)

For this case P(A \cap B) = P(c) =0.2, so if we replace we got:

P(A \cup B) =0.4 +0.8-0.2 =1.0

e. P(AnB)

The intersection between the set A and B is the element c so then we have this:

P(A \cap B) = P(c) =0.2

8 0
3 years ago
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