Find the limit as t approaches 8 for the function f(t)=7(t-1)(t-1)

Mathematics

1 answer:

Ratling [72]3 years ago

5 0

Answer:

7³

Step-by-step explanation:

You could answer this after a quick inspection. 7 remains constant as t approaches 8. Each of the (t -1) terms will approach 7. So, multiplying these factors together, you'll get 7(7)(7) = 7³3 as your answer, the limit as t approaches 8 of the given expression.

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Write a function rule for the statement.

ladessa [460]

The correct answers are: 
1) f(x)=1/2x;
2) f(x)=2x+1;
3) f(x)=x^3;
4) f(x)=6x.

Explanation: 
Let x be the input. In function notation, the output is denoted by f(x).

For #1, since the output is half of the input, we want to take half of x; this would give us
f (x)= $\frac{1}{2}$ x.

For #2, twice the input is 2x; one more than this is 2x+1, which gives us
f (x)=2x+1.

For #3, the cube of the input is x³, which gives us
f (x)=x³.

For #4, six times the input is 6x, which gives us
f (x)=6x.

3 0

3 years ago

Read 2 more answers

Find the dimensions of a rectangle with perimeter 108 m whose area is as large as possible. (If both values are the same number,

V125BC [204]

Answer:

27 by 27

Step-by-step explanation:

Let the sides be x and y. The problem is essentially asking:

Given 2(x+y)=108, maximize xy.

We know that x+y=54. By the Arithmetic Mean - Geometric Mean inequality, we can see that $\frac{x+y}{2} \ge \sqrt{xy$ . Substituting in x+y=54, we get $27\ge\sqrt{xy}$ , meaning that $729 \ge xy$ . Equality will only be obtained when x=y (in this case it will generate the maximum for xy), so setting x = y, we can see that x = y = 27. Hence, 27 is the answer you are looking for.