please explain steps to solution using excel. 3) Find the root(s) between -2 and 4 of the equation y xe sin(2x)-4 4) Integrate the function in problem 3 from 3 to 4.3 ne 4.3 3) Find the root(...

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Question

3) Find the root(s) between -2 and 4 of the equation y xe sin(2x)-4 4) Integrate the function in problem 3 from 3 to 4.3 ne 4

please explain steps to solution using excel.

math Advanced-Math

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Answer 1

Answer #1

3) Let

$f(x)e sin2r - 4$

$\therefore f'(x)=e^{x^2 \ sin2x}[x^2 \ cos2x + sin2x \ (2x)]$

now we use the Newton's formula to find root

$7t rn+1 =an f, (Zn)$

We use the following formulae in the excel sheet to do this task

the first cell B3 has a starting value -2

we then insert the following formula for the remaining cells of the first column , which is the Newtons formula

=B3-(C3/D3)

to find f(x) we insert the following formula,

=EXP((B4^2)*SIN(2*B4))-4

to find f'(x) we insert the following formula,

=EXP((B5^2)*SIN(2*B5))*((B5^2)*COS(2*B5)+SIN(2*B5)*(2*B5))

the following table is obtained

X	f(X)	f'(X)
-2	16.63957	-116.4439907
-1.85710	2.479718	-31.82297492
-1.77918	-0.39829	-15.61331576
-1.80469	0.343053	-19.69367324
-1.78727	-0.18027	-16.80410716
-1.79800	0.132826	-18.52796253
-1.79083	-0.07954	-17.35703206
-1.79541	0.054718	-18.09648888
-1.79239	-0.03445	-17.60505401
-1.79435	0.022997	-17.92152913
-1.79306	-0.01478	-17.71335332
-1.79390	0.00974	-17.84844907
-1.79335	-0.00631	-17.75998974
-1.79371	0.004138	-17.8175776
-1.79347	-0.00269	-17.77994458
-1.79363	0.00176	-17.80447665
-1.79353	-0.00115	-17.78845891
-1.79359	0.000749	-17.79890638
-1.79355	-0.00049	-17.7920874
-1.79358	0.000319	-17.7965361
-1.79356	-0.00021	-17.79363292
-1.79357	0.000136	-17.79552715
-1.79356	-8.9E-05	-17.79429107
-1.79357	5.78E-05	-17.7950976
-1.79356	-3.8E-05	-17.79457132
-1.79357	2.46E-05	-17.79491472
-1.79357	-1.6E-05	-17.79469064
-1.79357	1.05E-05	-17.79483686

Fro the table, the root is x = -1.79357

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Answer 2

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please explain steps to solution using excel. 3) Find the root(s) between -2 and 4 of the equation y xe sin(2x)-4 4) Integrate the function in problem 3 from 3 to 4.3 ne 4.3 3) Find the root(...