c) A thin wire of 5 cm length is heated with initial temperature profile f(x) = 1 – x² and its two ends are kept at a temperature of 0 °C. Assume the thermal diffusivity, k is equal to 1. Find the temperature distribution in the wire as a function of time. Show all the intermediate steps.

Q: 4. Find the equation of the tangent line to the graph of f(x)= 2x² – In Vx at x = 1.

A:

Q: 9) Suppose that the total cost of manufacturing x units of a certain commodity is C (x) = 2x? + 6x +…

A: Given function is as below : C(x)=2x2+6x+12 Marginal cost can be given by Derivative of C(x) .…

Q: Assumee thát ic COst C(x) = 25,600 + 100x + 0.01x² dollars to manufacture x 32GB iPods in a day. t…

A: given cost functio cx=25600+100x=0.1x2

Q: 3. Find an equation of the tangent line to the graph of y = log,x at the point ( 32,5).

A: We need to find the equation of the tangent line to the graph of y=log2x at the point (32,5) . Using…

Q: 1. FIND THE SLOPE OF THE TANGENT LINE TO THE GRAPH OF THE FUNCTION f(x) = 5 – x² AT (3,–4).

A: f(x)=5-x2 To find the slope of tangent, we can use two alternatives (1) Direct derivative (2)…

Q: 7. If the tangent line to y = f(x) at (-1,3) passes through the point (2,1), find fl-1) and f'(-1).

A:

Q: 1. Find the equation of the tangent and normal line to the curve f(x) =x' - 3x +2 at (1, 0).

A: Given the function f(x) :

Q: 3) Find an equation for the tangent line to the graph at the specified value of x. y=x²V5-x² ,x=1

A:

Q: Find a point c satisfying the conclusion of the MVT for the given function and interval. y = √x, [9,…

A:

Q: 2. Find the equation of the tangent and normal line of the function y+ 3xy +x = 5 at the point (1,…

A:

Q: Find a point c satisfying thr MVT for the given function and interval  y=x/x+2 [1,4]

A: Given query is to find the value of c.

Q: Find a point c satisfying the conclusion of the MVT for the given function and interval: y = ex − x,…

A:

Q: Find the equation for the line tangent to g(x) rcos(x) at x = 0

A: Given:The function g(x) = (x cos(x))/(x+2).Obtain the tangent line for the above function at x = 0.

Q: Find the number of units x that produces the minimum average cost per unit C (with a line over the…

A: We have to Find the number of units x that produces the minimum average cost per unit C (with a line…

Q: Find an equation of the tangent line to the graph at the given point .

A: Given: fx=4xx2+6 We need to find the equation of the tangent line to the graph f(x) at 2,45

Q: Find f(x) if f(2) = 3 and the tangent line at x has slope (x - 1)e** - 2x. f(x) = 1)et?

A: We have to find the function

Q: The slope of the line tangent to the graph of y = In(x²) at x = e² is %3D

A:

Q: 4. Find an equation of the line tangent to g(x) = 3x² - x +1 at x= 1.

A: Given function

Q: 1. Compute forward approximations of O(h) and O(h² for the first derivative of y = e* evaluated at x…

A: 1st we will derive formula for O(h) and O(h2) and then find corresponding values

Q: a) Show that if y = V1 + sin x then =: %3D b) A manufacturer estimates that x units of a particular…

A: NOTE: Refresh your page if you can't see any equations. . the demand function is  the revenue…

Q: The critical value(s) is(are) /Pound to two docimal places poodod Use

A: Given :  We have given that level of significance α=0.09

Q: 3. Estimate the derivative of the function, f(x) = cos x + tan1 x, at xi= 0.5 using Richardson's…

A: To find the derivative of the function fx at x=x0 by Richardson's extrapolation centered finite…

Q: 6. The slope of the line normal to the graph of y = 2 In(sec x) at x is 4

A:

Q: The equation of the tangent line to the graph of f(x) = vx+1 At the indicated point (3,2) is:…

A: The given function is fx=x+1. Evaluate the slope of the function at the point (3, 2) as follows.…

Q: Find an equation of the line tangent to the graph of the function: f(x) = V2x² – 1 at point P(-1;1).

A: Given:- f(x) = (2x2-1)(1/3)  To find:- Equation of tangent line at point p(-1, 1) on given curve

Q: 12. Find the x-coordinate of the point on the graph of y= Vx where the tangent line is parallel to…

A: From the given data: x=1 x=4

Q: 6. The tangent to the function f(x) = ke2x at x = has slope 2e. Find the value of k.

A:

Q: Find the minimum and maximum value of the function on the given interval by comparing values at the…

A: To find: The minimum and maximum value of the function on the given interval by comparing values at…

Q: 4. Find all points on the curve y = log (x³ – x) at which the tangent line is horizontal.

A: We will find all the points on the curve at which the tangent line is horizontal using calculus as…

Q: Determine the RMS Value of y=root x over the range of x=0 and x=1

A: We have to find the rms value of the given function over the given interval.     This problem can be…

Q: What is (V and find the relative minimum point as indicated by the black dot on the graph at the…

A:

Q: (4) Find the equation of the line tangent to f(x) = 12√ - 2² at the point (4,8).

A:

Q: 8) Find the equation of the tangent line to the graph of g(x) x3 7 at x = 2. -

A:

Q: 8. Find the point on the graph y = x³ where the tangent line is perpendicular to the line 3x +9y = 4

A: We have to find the point where tangent line is perpendicular to the line 3x+9y=4.

Q: 6. The slope of the line normal to the graph of y = 2 In(sec x) at x = is %3D

A: We need to find slope of normal line.

Q: 4) Determine the equation of the tangent line to the function 2 f(x) = x at the point (3, 9).

A:

Q: 7. Determine the equation of the tangent to the function E-2 f(x)=- at x= 1.

A:

Q: 4. Find the tangent line to the function f(x) =;xVx² + 5 at the point (2,2).

A: Tangent line of a function:  Differentiate the equation of the curve Substitute the value into the…

Q: 1- Find the average rate of change for y == Xo = 1 X1 = 2 2- Find the instantaneous rare of change…

A: Application of derivatives

Q: 3. Find the equation of the tangent line at point P(2,1) to the graph of the curve f(x) = V3x – 5

A: since you have posted multiple question in this question which are not interlinked so i have solved…

Q: 2) Find the tangent line to y2 = x at the point (4, –2).

A: Given: y2=x…

Q: Find an equation of the tangent line to the graph at the given point.

A: Given, fx=4xx2+6 Now we find the slope ddx4xx2+6 Now by using the quotient rule,…

Q: 3. Find the equation of the tangent line at point P(2,1) to the graph of the curve f(x) = v3x – 5

A:

Q: 12. If z = 2xy – 3x²y and x is increasing at 2 cm/s, determine at what rate y must be changing in…

A:

Q: Assume that it costs Apple approximately C(x) = 36,100 + 100x + 0.01x² dollars to manufacture x 32GB…

A: We use second derivative test to find out where cost is minimum

Q: Find the slope of the line tangent to the curve y = cos2 x at the point(−π/3 , 1/4)

A:

Q: Find the maximum slope on the graph of f(x, y) = 2 sin(ry) at the point P(4, 0).

A: The given question can be solved as shown in step2.

Q: 1- Find the equation of the tangent to the curve y= 2 sin x+ cos2x at the point x = n. 2- Find the…

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: Find the approximate value of derivative f'(0) with the step size h for the following function by…

A:

Q: Find the approximate value of derivative f'(0) with the step size h for the following function by…

A: