NO.1.(more...)
use the bisetion method to find the $p_3$ for $f(x)=\sqrt{x}-\cos x $ on $[0,1]$.
NO.2.(more...)
$f(x)=3(x+1)(x-\frac{1}{2})(x-1)$. Use the Bisection method on the following intervals to find $p_{3}$.
- $\left[-2,\ 1.5\right]$
- $\left[-1.25,\ 2.5\right]$
NO.3.(more...)
use the Bisection method to find solutions accurate to within $10^{-2}$ for $x^{3}-7x^{2}+14x-16=0$ on each interval.
- $\left[0,\ 1\right]$
- $\left[1,\ 3.2\right]$
- $\left[3.2,\ 4\right]$
NO.4.(more...)
use the Bisection method to find solutions accurate to within $10^{-2}$ for $x^{4}-2x^{3}-4x^{2}+x+4=0$ on each interval.
- $\left[-2,\ -1\right]$
- $\left[0,\ 2\right]$
- $\left[2,\ 3\right]$
- $\left[-1,\ 0\right]$
NO.5.(more...)
use the Bisection method to find solutions accurate to within $10^{-5}$ for the following problems.
- $x-2^{-x}=0$ for $0\leq x\leq 1$
- $e^{x}-x^2+3x-2=0$ for $0\leq x\leq 1$
- $x2\cos(2x)-(x+1)^{2}=0$ for $-3\leq x\leq-2$ and $-1\leq x\leq0$
- $x\cos x-2x^{2}+3x-1=0$ for $0.2\leq x\leq0.3$ and $1.2\leq x\leq1.3$
NO.6.(more...)
use the Bisection method to find solutions accurate to within $10^{-5}$ for the following problems.
- $3x-e^{x}=0$ for $1\leq x\leq2$
- $x+3\cos x-e^{x}=0$ for $0\leq x\leq1$
- $x^{2}-4x+4-\ln x=0$ for $1\leq x\leq2$ and $2\leq x\leq4$
- $x+1-2\sin\pi$x=0 for $0\leq x\leq0.5$ and $0.5\leq x\leq1$
NO.7.(more...)
sketch the graphs of $y=x$ and $y=2\sin x$. use the bisection method to find an approximation to within $10^{-5}$ to the first positive value of $x$ with $x=2\sin x$.
NO.8.(more...)
sketch the graphs of $y=x$ and $y=\tan x$. use the bisection method to find an approximation to within $10^{-5}$ to the first positive value of $x$ and $y=\tan x$.
NO.9.(more...)
sketch the graphs of $y=e^{x}-2$ and $y=\cos(e^{x}-2)$. use the bisection method to find an approximation to within $10^{-5}$ to a value in $\left[0.5,\ 1.5\right]$ with $e^{x}-2=\cos(e^{x}-2)$.
NO.10.(more...)
let $f(x)=(x+2)(x+1)^{2}x(x-1)^{3}(x-2)$, to which zero of $f$ does the bisection method converge when applied on the following intervals?
- $\left[-1.5,\ 2.5\right]$
- $\left[-0.5,\ 2.4\right]$
- $\left[-0.5,\ 3\right]$
- $\left[-3,\ -0.5\right]$
NO.11.(more...)
let $f(x)=(x+2)(x++1)x(x-1)^{3}(x-2)$, to which zero of $f$ does the bisection method converge when applied on the following intervals?
- $\left[-3,\ 2.5\right]$
- $\left[-2.5,\ 3\right]$
- $\left[-1.75,\ 1.5\right]$
- $\left[-1.5,\ 1.75\right]$
NO.12.(more...)
find an approximation to $\sqrt{3}$ correcto within $10^{-4}$ using the bisection algorithm. hint: consider $f(x)=x^{2}-3$.
NO.13.(more...)
find an approximation to $\sqrt[3]{25}$ correct to within $10^{-4}$ using the bisection algorithm.
NO.14.(more...)
use theorem 2.1 to find a bound for the number of iterations needed to achieve an approximation with accuracy $10^{-3}$ to the solution of $x^{3}+x-4=0$ lying in the interval $\left[1,\ 4\right]$, find an approximation to the root with this degree of accuracy.
NO.15.(more...)
use theorem 2.1 to find a bound for the number of iterations needed to achieve an approximation with accuracy $10^{-4}$ to the solution of $x^{3}-x-1=0$ lying in the interval $\left[1,\ 2\right]$, find an approximation to the root with this degree of accurracy.
NO.16.(more...)
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NO.18.(more...)
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NO.20.(more...)
