What is the laplace of L(f"(t))? A s2F (s) – sf (0) – f (0) B sF (s) - f(0) Osf (0) - f(0) D s2F(s) - sf (0) – f'(0)

Q: Calculate r' (t) and T(t), where r(t) = (6 +5t,9 – 61, 2t). r' (t) = ( ). T(t) = ( ).

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Q: Find f'(2), where f(t) f'(2) = = u(t) · v(t), u(2) = (2, 1, −2), u'(2) = (7, 1, 8), and v(t) = (t,…

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Q: Compute r''(t) and r'''(t) for the following function. r(t) = (9t2 + 3,t+ 1,1) = (9r?. Find r'(t).…

A: Find the first, second, and third derivative of the following vector-valued function. r(t) = <9t2…

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) = 3t³i + 6tj - t²k (a) r(t) (b) r"(t) (c)…

A: Given data÷

Q: (B) If f(x,t) = fakt e-y²dy, then prove that kfx = ft.

A: (.)  Leibniz rule :  Given

Q: (A) Suppose C= 4x²y + i3x³y? . Find divergence of C.

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Q: poin If g(u) —D V9u + 3 then g' (u) =

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Q: Find r'(t), r''(t), r'(t) · r''(t)

A: According to bartleby guidelines we supposed to do the first three subparts of multiple subparts…

Q: Minimizing the length of the residual vector r = b – Ax is equivalent of mini- mizing the quadratic…

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Q: (x* + y° ) In (x² + y* ). (x,y)= (0,0) f(x, y) = k +1, (x, y) = (0,0)

A: If f is continuous then lim (x, y) tends to (0, 0) =k+1 And using l hospital rule.

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). - r(t) = 3t²i – 4tj + ²t³k 2 (a) r' (t) (b)…

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Q: 2. Use the theorem in Sec. 23 to show that f'(z) and its derivative f"(z) exist everywhere, and find…

A: Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Determine fzz, fyy, and fz for f(x,y,z) = x²y³z – y sin(xz) + e».

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: Find r'(t), r"(t), r(t)•r"(t), and r'(t) × r'"(t). r(t)-흑러 - 26 + (a) r'(t) (b) r"(t) (c) r'(t) ·…

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Q: Find r'(t), r"(t), r(t) r"(t), and r(t) x r"(t). r(t) = 32²1 - 4tj + 12³k (a) r(t) (b) r"(t) (c)…

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Q: Let F (4t° + 2) i + sin(2t) j+ e*k Find F' (t), F"(t) and F" (t) (1) F'(t) (2) F"(t) (3) F"(t) =

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Q: Assume that R (t) + 0. Show that T'(1) = R' (t) – (De||R (t)|)Ť(t) T'(t : ||T (t)||

A: As per the question (and the general conventions in vector calculus) we have a vector valued curve…

Q: Suppose r'(t) has units of m/s. Explain why T(t) = r'(t)/ | r'(t) | is dimensionless (has no units)…

A: Suppose r'(t) has units of m/s. To explain why Let r(t) be a differential vector valued functionNow…

Q: If r(t) =  , find  r'(t), T(1), r''(t), and  r'(t) × r ''(t).

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Q: Let f(2) := 25. Show that f is invertible in a neighbourhood of i and calculate (f-1Y(/(i)).

A: Let f(z) = z5, show that f is invertible in a neighbourhood of i and calculate(f-1)' f(i)

Q: if f(z)=u(x,y)+iv(x,y)=z^2+3z+4 find u & v

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Q: alu,v at dx,yl Q2// B :- If u+v=e"cos y and u- v=e" sin y find the Jacobain of the function (х,у)…

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Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) × r"(t). r(t) = 2t²1 - 4tj + ²t³k (a) r(t) (b) r"(t) (c)…

A: Note that, according to Bartleby guidelines, we can answer only the first 3 sub-parts in the case of…

Q: (Calculus) The tangent vector to (x(t), y(t)) is (x'(t), y'(t)). The tangent vector's length ||(x',…

A: Given that the tangent vector to and is the speed of the point along the curve at time t .Here also…

Q: Find F(t) knowing that F'(t) = (t²,4t³, -t²) and F(0) = (0,1,0).

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Q: 0, 1) Knowing that u(t-a): |1, t<a =H¸ (t)=H(t-a)=u(t-a)=u̟ sketch the following tza functions. 1-a)…

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Q: Calculate r' (t) and T(t), where 88.8 r' (t) = ( T(t) = ( r(t) = (3t6,2 - 3t, 2t - 9).

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Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) = 2t²1 - 4tj + (a) r(t) (b) r"(t) (c)…

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Q: Find r'(t), r"(t), r'(t) r"(t), and r'(t) x r"(t). 1 t³ k 2 r(t) = 3t²1 – 3tj + 2 (a) r(t) (b) r"(t)…

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Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) = 5t²i - 5tj + 3t³k 2 (a) r(t) (b) r"(t)…

A: Note: As per the guidelines, I have solved three sub-parts. If you want the solution to the last…