Please find the general limit of the following function:
[tex]\lim_{x \to 9}(x^2 + 2^7 + (9.1 \times 10))[/tex]
Answers
Answer:
The general limit exists at x = 9 and is equal to 300.
Step-by-step explanation:
We want to find the general limit of the function:
[tex]\displaystyle \lim_{x \to 9}(x^2+2^7+(9.1\times 10))[/tex]
By definition, a general limit exists at a point if the two one-sided limits exist and are equivalent to each other.
So, let's find each one-sided limit: the left-hand side and the right-hand side.
The left-hand limit is given by:
[tex]\displaystyle \lim_{x \to 9^-}(x^2+2^7+(9.1 \times 10))[/tex]Since the given function is a polynomial, we can use direct substitution. This yields:
[tex]=(9)^2+2^7+(9.1\times 10)[/tex]
Evaluate:
[tex]300[/tex]
Therefore:
[tex]\displaystyle \lim_{x \to 9^-}(x^2+2^7+(9.1 \times 10))=300[/tex]
The right-hand limit is given by:
[tex]\displaystyle \lim_{x \to 9^+}(x^2+2^7+(9.1\times 10))[/tex]
Again, since the function is a polynomial, we can use direct substitution. This yields:
[tex]=(9)^2+2^7+(9.1\times 10)[/tex]
Evaluate:
[tex]=300[/tex]
Therefore:
[tex]\displaystyle \lim_{x \to 9^+}(x^2+2^7+(9.1\times 10))=300[/tex]
Thus, we can see that:
[tex]\displaystyle \lim_{x \to 9^-}(x^2+2^7+(9.1\times 10))=\displaystyle \lim_{x \to 9^+}(x^2+2^7+(9.1\times 10))=300[/tex]
Since the two-sided limits exist and are equivalent, the general limit of the function does exist at x = 9 and is equal to 300.
Step-by-step explanation:
Hey there!
Please look your required answer in picture.
Note: In left hand limit always take a smaller near number of the approaching number. For example as in the solution I took the 8.99,8.999 as it is smaller than 9 but very near to it.
And in right hand limit always take a smaller and just greater near number than the approaching number. For example, I took 9.01,9.001 which a just greater but very near to 9.
Hope it helps!
![Please Find The General Limit Of The Following Function:[tex]\lim_{x \to 9}(x^2 + 2^7 + (9.1 \times 10))[/tex]](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/VXEkDv7kz8vh9qpxMdJg0pkGvnX4gJ0D.jpeg)
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Have a nice day :)
ten un buen dia :)
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Answers
Answer:
length = 20
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Step-by-step explanation:
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Step-by-step explanation:
Given that :-
The perimeter of a rectangle is 54 cm. Its length and width if the length is represented by 3x + 2 and the width is represented by 2x – 5.To find :-
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Answer:
Step-by-step explanation:
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y= 35x/4
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The base of a solid right pyramid is a square with an
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VA
on(n-1) units
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(n-1)
n
Answers
Answer:
C
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What is the volume of a pyramid?The volume of a pyramid, is the product of the area of its base with the height of the pyramid, and divide by 3. We express this product with the formula V = ( 1/3) ×B×h, where B is the area of the base of the pyramid, and h is its height.
Volume of Pyramid = ( 1/3 )a²H
Given data ,
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On simplifying , we get
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Hence , the expression is V = ( 1/3 ) n² ( n - 1 ) units³
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O TRIGONOMETRIC FUNCTIONS
Arc length and central angle measure
Na
A circular arc has measure 18 in and is intercepted
a central angle of
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Do not round any intermediate computations, and round your answer to the nearest tenth.
?
Answers
Answer:
r = 22.9 in.
Step-by-step explanation:
Central angle in radians, ∅ = π/4
Length of arc, S = 18 in.
radius (r) = ?
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18 = r*π/4
18 = (πr)/4
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