Determine the interval (s) on which the vector-valued function r(t) = ti + Vt + 1j + (t2 + 1)k is continuous. O[-0, - 1) O[- 1, 0) O (- 1, 0) O[-0, 0)

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A: We can solve as follows

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A: Topic:- integration

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A: Given: r(t) = t2i +t5j Solution: r'(t) =ddtt2i+t5j =2t i +5t4j r"(t) =ddt2t i +5t4j= 2i + 20t3j

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A: answer is in next step

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A: Topic:- derivatives

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A: Solution:

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Q: im 2x² Sin 4x²

A: Given query is to find the limit of the expression.

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A: We have to find out

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A: Topic:- application of derivatives

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A: In this question we have to find the area.

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A: We need to find integral.

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A:

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A: We will differentiate partially with respect to x and y.

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A: The objective of the question is evaluate the limit.

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A:

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A: To Find : curl(4z i + 5x j +8y k)   Note that : If F=〈P,Q,R〉 is a vector field in ℝ3, and Px,Qy, and…

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A: We need to choose correct option.

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Q: Solve

A:

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A: The given laplace transform,  L15-3t

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A: We have to find correct option for the given questions.

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A:

Q: Use logarithmic differentiation to find

A: answer is in next step

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A: Apply the product rule of differentiation f·g'=f'·g+f·g' to find the derivative of the given…

Q: a) Determine the intersection points. b) Draw a sketch of the graph. c) Find the area of the region…

A:

Q: Find the four second partial derivatives. Observe that the second mixed partials are equal.…

A: Given that,      z=19xey-10ye-x

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A:

Q: Use Riemann Sums to calculate the area under the curve over the interval (1,3] for f(x) = x² + 2

A: By using Reimann Sums to calculate the area under the curve over the interval 1, 3 for fx=x2+2.

Q: 2) Find and of the following equation then simplify whenever possible. dx x = 1+ Sin t y = Cos? t

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A: We can solve as follows

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A: Find first partial derivative

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A: Given problem:-

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