1. Determine whether the vector-valued function 't² – 9 v - F(t) = t - 3 V3t – 1, t - 3 if t < 4, t # 3 In(4 – t), (6, 2, 1) if t = 3 is continuous at t = 3.

Q: (3) Evaluate the integral F. dr where the vector F is defined by F = and where the curve C is…

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Q: Compute the derivative of the vector valued functions. (a) Calculate the derivative in two different…

A: The solution are next step

Q: Q7:- Find the limit of the following vector functions:- (1) Lim (t²i+ 2tj) (2) Lim(+1i, (3) Lim (ti…

A: We have to find the limit of the vector function.

Q: 1. Determine the domain and range of the vector-valued function r(t) = (√t+3, In(2 – t), t²)

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Q: Find the limits of the following vector functions. 2t³-t² tan (2t)\ 21² (i) (ii) lim In 1-0 5t lim…

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Q: Find the domain of the vector-valued function. r(t) = n(t) 0 (-∞, +∞0) O (1, + ∞ ) O (0, +∞ ) O [1,…

A: Find the domain for all three components and then take intersection of those.

Q: Find the domain of r(t) and the interval(s) on which the vector- valued function is continuous. r…

A: We need to find the domain and the interval on which the vector-valued function is continuous.

Q: 1) Find the length of the function r = (1+ 2t, 3 – 2t, v2t²) on 0 <t < 1. %3D

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Q: In Exercises 61-67,firstfind f' and then find f.

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Q: 2. Consider the vector-valued function R(t) = { Show that is continuous at t = 1. (el-¹, 1-², In (2-…

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

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Q: 4. Consider the vector-valued function R(t) = a. Find the domain of R b. Show that R is continuous…

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Q: For what values of t is the vector-valued function, 7(t) = , continuous? | Domain: {t| <t< }

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Q: Consider the vector-valued function F(t) = exists. 21-6 In(-2) ²³-2t, 2-4t+3/ Find lim F(t), if it…

A: Here we have to find limit of given vector valued function.

Q: Find the limits of the following vector functions. -2) 21³-t² tan (21) 21²" (i) (ii) lim In 1-0 5t…

A: Since you have posted multiple questions, we are supposed to answer only first  question. If you…

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: 1.T.2 Let V be the set of all twice-differentiable functions f : R → R satisfying f"(x) = f(x) – 5.…

A: Let, f and g be two functions in V.  Then,        f"(x) = f(x) - 5       g"(x) = g(x) - 5.

Q: 21 Determine the domains of the vector-valued function r2(1) = (v/8 – 13, In 1, eviy %3D -

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Q: 1. Let V = C[-2, 2], the vector space of continuous functions on the closed interval [-2, 2). Let f,…

A: We can just multiply h and k and integrate  Then after simplifying we are getting answer

Q: 10. Let V be the vector space of functions spanned by B = {cos x – sin a, cos a + sin æ}. Find the…

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Q: x-1_y-2_z-1 -6 (c) show that the line 2 7 curve F(t) = (21+²) 1+ ²+ (in ²²-3) 1+1√21³²-1k at 1=1 i+…

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Q: 1.T.1 Let U be the set of all twice-differentiable functions f : R → R satisfying f"(x) + 2f'(x) –…

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Q: (a) Let v(t) be a differentiable vector valued function of t. If v. (dv/dt) = 0 for all t, can we…

A: The objective of the question is to determine if we can say anything about the magnitude of a vector…

Q: Find the values of real numbers a, b, and c such that the vector-valued function - {(at?, a(t + 1),…

A: A function f is continuous at x=a if

Q: (a) Let vt) be a differentiable vector valued function of t. If v. dy = 0 for all t, can we say…

A: The objective of the question is to determine if we can say anything about the magnitude of the…

Q: Let f : R" → R be a continuously differentiable function, while æ € R" is its non-stationary point…

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