A 10-cm copper wire with one end in an ice bath is heated at the other end, so that the temperature at each point x along the wire (in degrees Celsius) is given by T (x) = 50 cos πx 20 . Find the average temperature over the wire.

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Q: Find the antiderivative of f(x) = sin^2x

A: Antiderivative=∫sin2xdxsin2x=1−cos2x2So,∫sin2xdx=∫1−cos2x2dx=12∫1−cos2xdx=12∫1dx−∫cos2xdx=12x−∫cos2x…

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A: Since you have posted multiple questions but according to guidelines, we will solve first question…

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Q: Use an appropriate local linear approximation to estimate the value of the given quantity. Round…

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A: Here we have,  dvdt-15vtant5=20 given v(0)=1. Where v= velocity,  t = time

Q: Find the approximate value of f 10. ' to 4 decimal places using e su

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Q: B. Use the trapezium rule with 6 ordinates to estimate fe* dx correct to two decimal places.

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Q: (b)/ Use the Trapezoidal Rule with n = 4 to estimate (x' + 1)dx.

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Q: Find e dx approximately using Simpsons rule with n 10.

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Q: Use an appropriate local linear approximation to estimate the value of the given quantity. Round…

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Q: Find the most general antiderivative , verify answer by differentiation  g(x)=7sin theta/3

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Q: .A telegraph cable is made of an outer winding around an inner core. If x is defined as the core…

A: Using double derivative test to get max value of x

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A: Given : yx = sinxcosx

Q: If y = 1+ sin t ,x = cost at t == 2 Find- dt by using Chain Rule, then choose the correct answer:

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Q: 6. y = In (e* + e") 7. y = tan e + etanax 8. y = In(x + Vř +1) 9 y = Arctan(;

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Q: The height of an arch above the ground is given by the function y = 11 sin x for 0sxSr. What is the…

A: This question can be solved by applying the formula of average height of an arch.

Q: What is the first derivative of s(r) = log, sin z 712+8z+2 Provide your answer below: s'(x) =]

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Q: for the function f(x) = 2 cos(45x)o , determine:  the average rate of change for the interval 13  ≤…

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Q: The derivative of the function y = sin VE at a = is equal to %3D 4 14

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Q: The approximate value of dx by using Simpson's rule is 0.3480, then the error in the approximation…

A: Given Approximate value of the integral by Simpson's rule(Vs) = 0.3480 Now we will find the actual…

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Q: Find the average rate of change (AROC) of the following functions over the interval [60 ≤x≤180] y =…

A: using , average rate of change…

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A: As per bartleby guidelines we only give first question answers.

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A: Given that,

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Q: The height of an arch above theground is given by the function y = 10 sin x, for 0 ≤x ≤∏.What is the…

A: The height of an arch above the ground is given by the function y = 10 sin x, for 0 ≤x ≤∏.What is…

Q: Find the antiderivative of the function f(x) = - 4 sin (4x) when C = 0. The antiderivative is

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Q: Given the implicit function xy + yz = xz, find dz/dx by implicit differentiation

A: To solve by implicit differentiation

Q: Use an appropriate local linear approximation to estimate the value of the given quantity. Round…

A: cos32° It can be written as, cos32°=cos30°+2° Now, fx=cosx, x=30° & ∆x=2°=2π180 radians Now…

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A: The given function is  f(x)=sin x

Q: Use an appropriate local linear approximation to estimate the value of the given quantity. Round…

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Q: Find F dX, where x= 3 cost y= 1+3 sin 2r)

A: Given It has to find line integral of given parametrically curves Where

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A: Differentiate both sides with respect to t.

Q: The approximate value of| dx by using Simpson's rule is 0.3639, then the error in the approximation…

A: Approximate value of ∫161x4dx by using Simpson's rule is 0.3639 To find the error in the…