QuestionFind the value of the function $f(x) = x^{3}$ at $x = 5$ .

Studdy Solution

STEP 1

Assumptions1. The function f(x) is defined as $f(x) = x^{3}$ . The operation $\bigsqcup$ is a mathematical notation often used in set theory to denote the disjoint union of a collection of sets. However, in this context, it seems to be used as a summation symbol. We will assume it to be a summation symbol for the purpose of this problem.
3. The summation is from $x=1$ to $x=5$ , as no lower limit is provided, we will assume it starts from $x=1$ .

STEP 2

First, we need to find the value of the function $f(x)$ for each $x$ from1 to5.
$f(x) = x^{}$

STEP 3

Now, plug in the values for $x$ from1 to5 to calculate the value of $f(x)$ for each $x$ .
$f(1) =1^{3} =1$ $f(2) =2^{3} =8$ $f(3) =3^{3} =27$ $f() =^{3} =64$ $f(5) =5^{3} =125$

STEP 4

Now that we have the value of $f(x)$ for each $x$ from1 to, we can sum these values up to find the value of the given expression.
$\bigsqcup_{f(x)=x^{3}}^{x=} f(x) = f(1) + f(2) + f(3) + f(4) + f()$

STEP 5

Plug in the values for $f(1)$ , $f(2)$ , $f(3)$ , $f(4)$ , and $f(5)$ to calculate the sum.
$\bigsqcup_{f(x)=x^{3}}^{x=5} f(x) =1 +8 +27 +64 +125$

STEP 6

Calculate the sum.
$\bigsqcup_{f(x)=x^{3}}^{x=5} f(x) =1 +8 +27 +64 +125 =225$ The value of the given expression is225.

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QuestionFind the value of the function $f(x) = x^{3}$ at $x = 5$ .

Studdy Solution

STEP 1

STEP 2

First, we need to find the value of the function $f(x)$ for each $x$ from1 to5.
$f(x) = x^{}$

STEP 3

Now, plug in the values for $x$ from1 to5 to calculate the value of $f(x)$ for each $x$ .
$f(1) =1^{3} =1$ $f(2) =2^{3} =8$ $f(3) =3^{3} =27$ $f() =^{3} =64$ $f(5) =5^{3} =125$

STEP 4

Now that we have the value of $f(x)$ for each $x$ from1 to, we can sum these values up to find the value of the given expression.
$\bigsqcup_{f(x)=x^{3}}^{x=} f(x) = f(1) + f(2) + f(3) + f(4) + f()$

STEP 5

Plug in the values for $f(1)$ , $f(2)$ , $f(3)$ , $f(4)$ , and $f(5)$ to calculate the sum.
$\bigsqcup_{f(x)=x^{3}}^{x=5} f(x) =1 +8 +27 +64 +125$

STEP 6

Calculate the sum.
$\bigsqcup_{f(x)=x^{3}}^{x=5} f(x) =1 +8 +27 +64 +125 =225$ The value of the given expression is225.

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QuestionFind the value of the function f(x)=x3f(x) = x^{3}f(x)=x3 at x=5x = 5x=5.

Studdy Solution

STEP 1

STEP 2

First, we need to find the value of the function f(x)f(x)f(x) for each xxx from1 to5.f(x)=xf(x) = x^{}f(x)=x

STEP 3

Now, plug in the values for xxx from1 to5 to calculate the value of f(x)f(x)f(x) for each xxx.f(1)=13=1f(1) =1^{3} =1f(1)=13=1f(2)=23=8f(2) =2^{3} =8f(2)=23=8f(3)=33=27f(3) =3^{3} =27f(3)=33=27f()=3=64f() =^{3} =64f()=3=64f(5)=53=125f(5) =5^{3} =125f(5)=53=125

STEP 4

Now that we have the value of f(x)f(x)f(x) for each xxx from1 to, we can sum these values up to find the value of the given expression.⨆f(x)=x3x=f(x)=f(1)+f(2)+f(3)+f(4)+f()\bigsqcup_{f(x)=x^{3}}^{x=} f(x) = f(1) + f(2) + f(3) + f(4) + f()f(x)=x3⨆x=​f(x)=f(1)+f(2)+f(3)+f(4)+f()

STEP 5

Plug in the values for f(1)f(1)f(1), f(2)f(2)f(2), f(3)f(3)f(3), f(4)f(4)f(4), and f(5)f(5)f(5) to calculate the sum.⨆f(x)=x3x=5f(x)=1+8+27+64+125\bigsqcup_{f(x)=x^{3}}^{x=5} f(x) =1 +8 +27 +64 +125f(x)=x3⨆x=5​f(x)=1+8+27+64+125

STEP 6

Calculate the sum.⨆f(x)=x3x=5f(x)=1+8+27+64+125=225\bigsqcup_{f(x)=x^{3}}^{x=5} f(x) =1 +8 +27 +64 +125 =225f(x)=x3⨆x=5​f(x)=1+8+27+64+125=225The value of the given expression is225.

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QuestionFind the value of the function $f(x) = x^{3}$ at $x = 5$ .

First, we need to find the value of the function $f(x)$ for each $x$ from1 to5.
$f(x) = x^{}$

Now, plug in the values for $x$ from1 to5 to calculate the value of $f(x)$ for each $x$ .
$f(1) =1^{3} =1$ $f(2) =2^{3} =8$ $f(3) =3^{3} =27$ $f() =^{3} =64$ $f(5) =5^{3} =125$

Now that we have the value of $f(x)$ for each $x$ from1 to, we can sum these values up to find the value of the given expression.
$\bigsqcup_{f(x)=x^{3}}^{x=} f(x) = f(1) + f(2) + f(3) + f(4) + f()$

Plug in the values for $f(1)$ , $f(2)$ , $f(3)$ , $f(4)$ , and $f(5)$ to calculate the sum.
$\bigsqcup_{f(x)=x^{3}}^{x=5} f(x) =1 +8 +27 +64 +125$

Calculate the sum.
$\bigsqcup_{f(x)=x^{3}}^{x=5} f(x) =1 +8 +27 +64 +125 =225$ The value of the given expression is225.