5. Use the laplace transform to solve the. definite solution problem S Ut - αlx =0, x>0, t>o uro, t) = cost, tzo U(X₂O) = Ut (X.0)=0- X=0 U(x, t) is bounded.

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

A: Given,

Q: 2 (y – k) y' = 4a Find the Derivative - d/dy Since 4a is constant with respect to y, the derivative…

A: (1). The given expression is:2y-ky'=4a

Q: 2. The pdf of (X,Y) is 1 еxp TV3 fzy(x, y) ry+ 3 x<x < o, -00 < y < 0 Find the regression curve of Y…

A:

Q: IT ) Verify that ,0) is a critical point of f(x, y) = y² - 2y cos x. Then use the second derivative…

A:

Q: Eliminate the paranoter t from the follewing S r(1) = 4+ sin t lu(t) 3- cost

A:

Q: Given f(x, y) = 2x3 – 3y? – 6xy %3D (i) Find critical points of f. (ii) Use the second derivative…

A: Given that,f(x, y)=2x3-3y2-6xy-12x

Q: ху +8x*yVz find the partial derivative Wgyz 2. Given w =In %3D

A:

Q: 13. Find ƒ. (1)ƒ'(x)=x² + 3√x (2) f(t)=2cost+sec²t,-/2 <t</2,ƒ(π/3)=4; (3)ƒ*(x) = 6x+sinx.

A:

Q: Let f(x, y) = x2 – y?. Find (a) The directional derivative of f at (-2, 1) in the direction of v = i…

A:

Q: 2. Let closed curve C consist of the line segment from (0,0) to (2, 1), followed by the line segment…

A: We will solve both the parts using the basics of integral calculus, in particular double integral,…

Q: Q3: Find gradient of the following function at given point f(x, y. =) = (x² + y° + :')"? + In(xyz).…

A: The detailed solution is as follows below:

Q: Just use the definition L{f (t)} = ° e-st f (t) dt with 2 integrals, one for 0 1

A: Laplace transferom

Q: f(x,y) be defined implicitly as a function of x and y by the 3xyz =exyz Əz Əz yay ax Əz Əz Find and…

A:

Q: 5. Find the gradient of cos(xy) – 3y* + 3 at the point (1,4)

A:

Q: consider the function f(x)=x4-5x3+8x2+5x+7 compute the linear approximation Lf,1(x). Check that its…

A:

Q: 4 a. Consider the i.v.p x' = t^(2) + cos(x), x(0) = 0. Verify that the hypothesis of Cauchy Picard…

A:

Q: 1. Find the critical points of f (x,y) = 8y³ + x³ – 6xy and use the second derivative test to…

A:

Q: f(r, y, z) = sec='(9x + 3yz) f. = fy = f; =

A:

Q: 4 a. Consider the i.v.p x' = t^(2) + cos(x), x(0) = 0. Verify that the hypothesis of Cauchy Picard…

A: a. Verifying Conditions of Cauchy-Picard Theorem  b. Estimating the Interval of Existence

Q: 26. Evaluate the gradint of f (x,y,₁z) = log (= ² + y² +₂²) at (1₁91)-11

A:

Q: Find the partial derivative Əz Əx for the function z = 8y²√x.

A:

Q: Let h(y) = (2y – 3)4 Determine the derivative of h. h'(y) 8 (2y-3) 5 ✓ h is differentiable on 05…

A:

Q: (t²,0 2 7. in terms of unit step function, hence obtain LT. %3D

A:

Q: Find the maximum slope on the graph of f(x, y) = 4 sin(xy) at the point P(5, 0). 1. max slope 20T 2.…

A: Given:- f(x, y) = 4 sin(xy) To find:- Find the maximum slope on the graph of f(x, y) = 4 sin(xy) at…

Q: Suppose f(x) = [ 6t² /1+t° dt .

A:

Q: (3) Consider the derivative: 2xydx + (x² + 2y)dy. Evaluate whether this is a total derivative or an…

A: We will check whether the given function is total derivative or not. Consider dz = (2xy)dx + (x 2 +…

Q: Let f(x, y) = x³ + 2ry – y² be a func the tangent plane to f(x, y) at the poi

A: Here we have f(x,y)=x3+2xy-y2  we have to find the equation of the tangent plane to f(x,y) at point…

Q: Let f(x) = х+ 1 (a) Evaluate f(0), f(3), and f(a + 3). f(0) : V3 f(3) 4 f(а + 3). (b) Find the…

A: Topic -functions qnd average rate of change of function over certain interval

Q: Find f' and f" for the function. f(t) 92²2²-7 t f'(t) F"(t) = 18t + 7 انا 2 14 18+ + X X

A: Given: f(t)=9t2-7t

Q: 4. Use Laplace transforms to solve the following initial value problems. (a) y"+2y-3y = 10 sinh 2t,…

A: Laplace transform.

Q: 5. (а) Find the directional derivative of f at P in the direction of ā if f(x,y) = y In(x) ; P(1,4);…

A: To find The directional derivative of f at p in the direction of a.