Solve the following Cauchy problem on half-line: Utt = Uxx u (0, t) = 0, u(x, 0) = x, ut(x, 0) = sinx, x > 0, t > 0, t> 0, x > 0,

Q: It is the tangent line at the point (2,4) to the curve x3 y3-9xy = 0 5y = 4x+5 5y = 12x+4 5y=4x+12…

A: Step 1:Given curve: x3+y3−9xy=0Point: (2,4)We have to find the equation of the tangent line at the…

Q: Show that the directiona f(x, y, z) = z²x + y ² at ( X (1/15" + ) ; 255. them

A: fx,y,z=z2x+y3 P1,1,2v→=15i+25j We know directional derivative Dv→fP=∇fP.v→v→

Q: Find the length of the hyperbolic function y = cosh x from (0,1) to (8, cosh 8)

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Q: The equation x''+ x = sin t has a bounded solution. true or false ?

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Q: Pron a. If u = f(x, y), where r = e' cost, and y = e' sint, show that (3)³ + (3) ² - - ² [(-)* +…

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Q: Let f(1) = (1 + 2x + 2)*

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Q: 6) If y=x² +1+ f dt , prove that y"= 2 - x2

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Q: Prove that da(x) = a(b) a(a), %3D |

A: This is a problem from Reimann Stieltzes Integral

Q: et f(x,y)= x^2-xy+y^2-y   what are the min and max values of Du f(1,-1)?

A: Given :  f(x,y) = x2-xy+y²-y  To find :  Maximum and minimum values of directional derivative at…

Q: Compute ∫C(2x+√y)ds, where Cis the curve from (0,0) to (2,4) along y=x^2.

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Q: 3. If f is the function given by f(x) = -x³ + x² + 3x-2, name the open interval where the graph of f…

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Q: The equation of the line tangent to the curve F (x) = S e dt at a = %3D V1- O y-V2 = (=- ) O %3D y -…

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