Mathematics : asked on zoey130
 24.05.2023

The table above gives values of the differentiable functions f and g and their derivatives at x=2. If h(x) = (4f(x))/(g(x)+1), then h'(2)=

. 7

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Mathematics
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P Answered by Specialist

Check your given table for the value of x such that f(x) = 4. Then x = g(4), and by the inverse function theorem,

g'(4) = \dfrac1{f'(x)} = \dfrac1{f'(g(4))}

Mathematics
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P Answered by Specialist

The required value of \int\limits^4_2 {f(x)g"(x)} \, dx (1) is 63.

Given that,

The table above gives selected values of twice-differentiable functions f and g,

The first two derivatives of g. If f′ (x) = 3 for all values of x.

We have to determine,

What is the value of \int\limits^4_2 {f(x)g"(x)} \, dx (1).

According to the question,

To obtain the value of given function, integrating the function,

= \int\limits^4_2 {f(x)g"(x)} \, dx (1)

Integrating by using by-parts.

= \int\limits^4_2 {f(x)g"(x)} \, dx (1)\\\\if\  u = f(x), \ then \ du = f'(x)dx\\\\if \ dv = g"(x)dx, \ then \  v = g'(x)\\\\

Then,

\int u\ dv = uv\ - \ \int v \ du\\\\= f(x) \ g'(x) - \int g'(x) f'(x) \ dx\\

if f'(x) is constant at 3,

Then,

= f(x) g'(x) - \int g'(x)\dx\\\\= f(x) g'(x) -3g(x)

Substitute from x = 2 to x = 4 then evaluate,

= [f(4)\ g'(4) - 3 \ g (4)]- [f(2)\ g'(2) - 3 \ g (2)]\\\\= [(13).(7) - 3.(9)] - [7.(1)- 3.(2)]\\\\= [91-27} - {7-6}\\\\= 64-1\\\\= 63

Hence, The required value of \int\limits^4_2 {f(x)g"(x)} \, dx (1) is 63.

To know more about Integration click the link given below.

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Mathematics
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P Answered by PhD

The answer is in the image 

The answer is in the image 
Mathematics
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P Answered by PhD

The solution is in the following image

The solution is in the following image
Mathematics
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P Answered by PhD

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

Mathematics
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P Answered by PhD

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

Approximately it is aqual to 1300kg

Mathematics
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P Answered by PhD

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

Mathematics
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P Answered by PhD

Speed=Distance/time

Here,

distance=15m

time=1sec

speed=15/1=15m/sec

Distance=Speed*time

time=15min=15*60sec=900sec

Distance travelled in 15 min=15*900=13,500m

=13500/1000 km=13.5Km

Mathematics
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P Answered by PhD

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

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