(a) Model the temperature distribution in a bar of length π with diffusivity 4; and the ends x = 0 and x = π are insulated. The initial temperature is f(x)=sin(x). (b) Derive the temperature distribution from the equation you modelled in part (a).

Q: Find a formula for the curve y = f (2) given that its slope at the point (x, y) is y² (2+ sin x) and…

A:

Q: On a particular summer day the temperature function in Celsius is given by (7) T(t+7) T(t) = 20 + 8…

A: The function f(t) is a rule that associates or fixes a number to the particular point t. If the…

Q: Q1. (а) Sketch the graphs and find the domain and range of the following functions: Coi () у 3D Vx —…

A: Range and domain of given graph is given : y= sqrt(x-5)  y = 1/(x-2)

Q: 2.x²y"+xy'–3y= 0,x>0

A:

Q: 1: For each of the functions below, decide whether it solves the equation: (y)² = 1 - y². A) y(t) =…

A: Given that the differential equation is .The objective is to verify the given solutions.

Q: c. _h(x) = e¯³(sin(x) + 2x); only quotient rule

A: To solve the following using quotient rule

Q: X(t) = b cos(wt) + V a² – b² sin²(wt)

A: We will use differentiation rules to solve this question.

Q: - Find sec(y) tan7 (y) dy. S .

A:

Q: What is the line that corresponds to the phase shift of the function f(x)=tan (π/2 x−3π/2) +4?

A:

Q: The owner of a skating rink rents the rink for parties at $240 if 20 or fewer skaters attend, so…

A:

Q: Given x = 5t - 5 and y = 25 sin t dy da t-0 (ii) dy da 2 t-0

A:

Q: 6. A sensor is attached to a spring and its velocity is given by the function v(t) = cos(2t) feet…

A: Derivative of velocity function gives displacement function of a body.

Q: 2. The slope of a curve at any point (x, y) is given by dy da 4x, if the curve passes through (-1,…

A:

Q: Show your complete solution

A: We will find the derivative using Chain rule.

Q: dy 3. Plot the slope field for the differential equation dx = y2 – x and sketch the solution for the…

A: Introduction: Slope fields (also known as direction fields) are a graphical representation of the…

Q: Find the value(s) of ß for which y (t) = cos(ßt) satisfies y” + 100y = 0

A: Given that yt=cosβt satisfies the equation y''+100y=0. We have to find the values of β.

Q: 3x 3x A Math 31 student discovers that y' = sin- and she wishes to know where the cos function y =…

A:

Q: Find the general solution of the differential equation y" - 2y' - 63y = -181t + 126t². NOTE: Use t…

A:

Q: B) Find for the Implicit function: dx x? – sin(xy) + y? = 5xy

A: The given equation is; x2-sin(xy)+y2=5xy.

Q: Determine the derivative -d/dv y = 2x³ + 5x - 6 y 1 x² 3x 6x³ + x² − 10x − 3 -

A:

Q: -5 #2. Suppose that S„ƒ(x)dx= 6 andS²,g(x)dx= -4. Find S°,[3f(x) – 0.5g(x)]dx.

A: To evaluate the given integral apply the following rules.