3. Consider the initial valve problem for U = U(t, x) for XER given by Ut + UU x = 0, U (0,x) = 1+ x² Write down a formula for the characteristic line that goes through the point y on the x-axis. sketch some of the characteristic lines in the (t,x)- plane calculate the critical time, t*, at which the solution, u, develops a vertical tangent line. Use the method of characteristics to sketch the Solution as a function of X just before and just after the critical time (Just after the critical time interpret the solution as a multivalved function)

Q: In explicit method of hyperbolic PDES, the second initial condition, the one involving g, gives…

A: Given,

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A: Given equation: f(x)= 2x4- 5x f(1)= 2(1)4- 5(1)= -3

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A:

Q: given point 1. y = 2x° - 3x² - 2x + 5 ; where x 1

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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A:

Q: The tangent line to y = f(x) at (1,—8) passes through the point (9,-7). Compute the following. a.)…

A: We can solve this as follows:

Q: 1 Find an equation of the tangent to the curve f(x) = /x + 8 that has slope 4 %3D - OA. 1 y =7x-3 O…

A: Equation of the line in slope-point form is:        m = slope (x1, y1) = point on the line

Q: Find the equation of the tangent line and normal line to the graph of y = x-1 at the x+1 point where…

A:

Q: L et f(x)= x- 3x and P= (1, f (1)). Find (a) the slope of the curve y = f(x) at P, (b) an equation…

A: The given function is fx=x2-3x and the point is P=1, f1. Evaluate f(1) as follows. f1=12-31=1-3=-2…

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A: Solve the given problem.

Q: 3) Find all points (x, y) on the graph of x2/3+y²/3 = 8 where the tangent lines have slope –1.

A:

Q: 5. Find the derivative of y = In(cos v3x + 2 ), by using chain Rule.

A:

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A:

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A: As we know that: The slope of the tangent line to the given curve is equal to the derivative of the…

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A:

Q: Find an equation of the tangent plane to the graph y = x² + 2xz at (1,3, 1). (Possible Answer: 4r –…

A: We have to find an equation of the tangent plane to the graph y=x2+2xz at 1,3,1.

Q: Find the equation of the tangent line to the curve y = Oy=3e-³x+3e-² Oy=-3e-³x+6e-¹ Oy=3e ³x-3e-²…

A: