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3 years ago

Calculus 1 question I need help with

Mathematics

1 answer:

kotykmax [81]3 years ago

6 0

Answer:

Step-by-step explanation:

f(x) = e^(8x⁵−8x)

Since f(x) is continuous:

lim(x→1) f(x) = f(1)

lim(x→1) f(x) = 1

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Each time Shelley goes tobthe store she likes to buy gum.She buys one pack for $1.00 and then another pack for $0.50 more.How mu

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$2.50

Step-by-step explanation:

Shelley buys one pack of gum for $1

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1 + 0.50 = 1.5

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2 years ago

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2 years ago

What will be the result of substituting 2 for x in both expressions below?

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3 years ago

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3 years ago

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I really need help with this. Can anyone help me please?

I am Lyosha [343]

Answer:

$f(x)=(x-3)(x^2+4x+8)$

Step-by-step explanation:

A polynomial function is given by the form:

$f(x)=a(x-p)(x-q)...$

Where a is the leading coefficient, and p and q are the roots (more can be added if necessary).

Our zeros are 3 and (-2 + 2i).

And our leading coefficient a = 1.

Furthermore, by the Complex Root Theorem, if (-2 + 2i) is a zero, then (-2 - 2i) must also be a zero.

So, by substitution, we acquire:

$f(x)=1(x-(3))(x-(-2+2i))(x-(-2-2i))$

Simplify:

$f(x)=(x-3)(x+2-2i)(x+2+2i)$

Expand the second and third factors:

$\begin{aligned} &=(x+2-2i)x+(x+2-2i)(2)+(x+2-2i)(2i)\\&= (x^2+2x-2ix)+(2x+4-4i)+(2ix+4i-4i^2)\\&=(x^2)+(2x+2x)+(-2ix+2ix)+(-4i+4i)+(4-4i^2)\\&=x^2+4x+(4+4)\\&=x^2+4x+8 \end{aligned}$

Therefore, our polynomial function of least degree and the given zeros will be:

$f(x)=(x-3)(x^2+4x+8)$

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2 years ago