55. By the transform method, solve Ut = Urx + g (x,t), u (x, 0) = f (x), 0 < x < T, t > 0, 0 0.

Q: If f(x) = f'(x) = 1 x³ 3 √t² + 1 dt then F

A: Here we will use the Leibniz theorem to  find the derivative of the given problem, so on using this…

Q: From the previous page: the function f(x) = e*(x² + x – 1) has derivatives f'(x) = e*(x² + 3x),…

A: Consider the following function: fx=exx2+x-1f'x=exx2+3x Consider the part (e): Linear approximation…

Q: √²³₁(−12xy² + 8x³y + 3)dxdy

A: LetWe have to evaluate the above integral.

Q: Let f(t) 3t* Then f'(t) = 7t + 7e'.

A: SOLUTION-

Q: Let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. Find r'(1) and s'(4).…

A: our objective is to find the required derivative

Q: d/dt (t2 + 1/t + 1)

A: Given ddtt2+1t+1

Q: DEFINITION 10.1.1 Let f be a function defined on an interval [0, o0). The Laplace transform of f is…

A: Lapalce transfermation.

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

A:

Q: f (x) = 2x+7 if -5=Xcl 8 If X = 1 14X=3 if 11x-2 31 If x > 3 IS this continuous at X=1 ? formula…

A: Any function f(x) is continuous at x=a if  lim x -&gt; a f(x) = f(a) i.e. Functional value at that…

Q: Define diffeomorphish between two manifolds and Completly explain why any linear map fiM_N. between…

A:

Q: Show that P2(x) = f(a) + f'(a)(x − a) + c2(x − a)2 for each value of c2 satisfies the requirements…

A:

Q: Find of z = In(xy)

A: Given,Z=ln(xy)differentiating both the sides partially w.r.t. x∂z∂x=1xyy1∂z∂x=1xagain differntiating…

Q: Let f(t) = 3t – 8t + 5e'. - Then f'(t) =

A:

Q: Let f(t) = 4t* – 4t + 5e'. Then f'(t) =

A: find the derivative

Q: f(t) = (t + 4t + 8)(7t¯² + 6t).

A: Given function is: ft=t2+4t+87t-2+6t-3 Then we get,…

Q: Display the discontinuity of h at (0,0) and Evaluate hx(0,0).

A:

Q: In problem (A), find a linear approximation f(x, y) at the indicated point. (x + y)´| at (-1,1) A)…

A:

Q: Compute N(0) if r(t)= and prove that T(0) and N(0) are orthogonal

A: Given rt=&lt;t sin t+cos t,2t2,sin t -t cos y&gt; Then vector is given by r→t=t sin t+cos…

Q: determine the singular points of the given function, type of these points and calculate their…

A: The given function is                                      f(z)=1z2-4z+13

Q: y The function f(x, y)= (2x* + y* )exp + xy' is homogenous in x and y of degree 2x

A: Follow the procedure given below.

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

A:

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

A:

Q: Find ƒ if ƒ' (t) = 5 csc(t) (csc(t) + 2 cot(t)), 0 < t < π, and ƒ (7) f f(t) = = -10√/2

A:

Q: f"(x) = 20x3 + 12x2 + 4 with the initial conditions f(0) particular f(x). = 8 and f(1) = 5. Det

A:

Q: 8. Find f(4) if f(0) >0 and [f(x)]² = [(f(t))² + (f'(t))²]dt + 4.

A: We do this using Lebniz rule for differentiation under integral sign. The detailed solution is…

Q: 5. If f (x) = (x + 1)(x2 – 2)3 then f'(x) da व्य 2= 2x (1) 2 A. & 6xx2 – 2)2 انی + (22 21 2 = Alv 3x…

A: Given query is to find the derivative of the function.

Q: Sa cos(r) dr = ,2 %3D 1 sin(r³) +c cos(r³) + c -1 - sin(r*) + c 3 cos(r³) + c 3 1/3

A:

Q: b\ Find the domain of the functions: (1) y = (2) y = = (3)f(x) =

A:

Q: Determine each of the following derivative values that involve functions that are defined in terms…

A:

Q: 10. Integral 2-t dt

A: