Chapter 1.2, Problem 1E

a.

To determine

To show: The equation $x\cos x-2x^2+3x-1=0$ has at least one solution in the intervals $\left[0.2,0.3\right]$ and $\left[1.2,1.3\right]$ .

b.

To determine

To show: The equation ${\left(x-2\right)}^2-\ln x=0$ has at least one solution in the intervals $\left[1,2\right]$ and $\left[e,4\right]$ .

c.

To determine

To show: The equation $2x\cos \left(2x\right)-{\left(x-2\right)}^2=0$ has at least one solution in the intervals $\left[2,3\right]$ and $\left[3,4\right]$ .

d.

To determine

To show: The equation $x-{\left(\ln x\right)}^x=0$ has at least one solution in the interval $\left[4,5\right]$ .