From the graph ⇒ f(-4) = -8
⇒ f(x) = 2x
Answer:
a) {2/n²-7/n+9}/{8+2/n-6/n²}
b) 9/8
c) The sequence converges
Step-by-step explanation:
Given the limit of the function
limn→[infinity]2−7n+9n²/8n²+2n−6
To simplify the function given, we will have to factor out the highest power of n which is n² from the numerator and the denominator. The function will then become;
2−7n+9n²/8n²+2n−6
= n²{2/n²-7/n+9}/n²{8+2/n-6/n²}
The n² at the numerator will then cancel out the n² at the denominator to have resulting simplified equation as;
{2/n²-7/n+9}/{8+2/n-6/n²}
Evaluating the limit of the resulting equation will give;
limn→[infinity] {2/n²-7/n+9}/{8+2/n-6/n²}
Note that limn→[infinity] a/n = 0 where a is any constant.
Therefore;
limn→[infinity] {2/n²-7/n+9}/{8+2/n-6/n²}
= (0-0+9)/(8+0-0)
= 9/8
Since the limit of the sequence gives a finite value which is 9/8, thus the sequence in question is a convergent sequence.
The limit of a sequence only diverges if the limit of such sequence is an infinite value.
Answer:
1over3
Step-by-step explanation:
number of successful outs come over the total number 5over 15
Answer:4
Step-by-step explanation:
B) -7x-2x= -20-16
-9x= -36
X= -36 /-9
X= 4
Answer:
Width = 2x²
Length = 7x² + 3
Step-by-step explanation:
∵ The area of a rectangle is 
∵ Its width is the greatest common monomial factor of 
and 6x²
- Let us find the greatest common factor of 14 , 6 and 
, x²
∵ The factors of 14 are 1, 2, 7, 14
∵ The factors of 6 are 1, 2, 3, 6
∵ The common factors of 14 and 6 are 1, 2
∵ The greatest one is 2
∴ The greatest common factor of 14 and 6 is 2
- The greatest common factor of monomials is the variable with
the smallest power
∴ The greatest common factor of and x² is x²
∴ The greatest common monomial factor of and 6x² is 2x²
∴ The width of the rectangle is 2x²
To find the length divide the area by the width
∵ The area =
∵ The width = 2x²
∴ The length = ( ) ÷ (2x²)
∵ ÷ 2x² = 7x²
∵ 6x² ÷ 2x² = 3
∴ ( ) ÷ (2x²) = 7x² + 3
∴ The length of the rectangle is 7x² + 3
