/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 60 Evaluate \(\frac{x^{2}+11}{3-x}\... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 60

Evaluate \(\frac{x^{2}+11}{3-x}\) for \(x=4 i\)

Short Answer

Expert verified
The value of the function at \(x=4 i\) is \(-0.6-0.8i\)

Step by step solution

01

Substitution

Substitute \(x=4i\) into the function to get \(\frac{(4i)^{2}+11}{3-4i}\)
02

Simplification of numerator

Simplify the numerator by squaring \(4i\) to obtain \((-16)+11\) in the numerator, which gives \(-5\). The function now becomes \(\frac{-5}{3-4i}\)
03

Multiplication by conjugate

To eliminate the imaginary number on the bottom, multiply both the numerator and the denominator by the conjugate \(3+4i\). This gives \(\frac{-5(3+4i)}{(3-4i)(3+4i)}\)
04

Simplification

Expand by distributing both the numerator and denominator to get \(-15-20i\) in the numerator and \(9+16\) on the denominator to give \(\frac{-15-20i}{25}\)
05

Division

Finally divide all the terms in the numerator by the denominator: \(-15 \div 25 = -0.6,\) and \(-20i \div 25 = -0.8i\). So, \(\frac{-15-20i}{25} = -0.6-0.8i\)

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Most popular questions from this chapter

The equation for \(f\) is given by the simplified expression that results after performing the indicated operation. Write the equation for \(f\) and then graph the function. $$\frac{5 x^{2}}{x^{2}-4} \cdot \frac{x^{2}+4 x+4}{10 x^{3}}$$

Use transformations of \(f(x)=\frac{1}{x}\) or \(f(x)=\frac{1}{x^{2}}\) to graph each rational function. $$(x)=\frac{1}{(x+2)^{2}}$$

a. Find the slant asymptote of the graph of each rational function and \(\mathbf{b} .\) Follow the seven-step strategy and use the slant asymptote to graph each rational function. $$f(x)=\frac{x^{3}+1}{x^{2}+2 x}$$

Use everyday language to describe the behavior of a graph near its vertical asymptote if \(f(x) \rightarrow \infty\) as \(x \rightarrow-2^{-}\) and \(f(x) \rightarrow-\infty\) as \(x \rightarrow-2^{+}\).

If you are given the equation of a rational function, explain how to find the vertical asymptotes, if any, of the function's graph.
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