Find r(t). u(t). r(t) = (3t − 4)i + ¹1t³j + 4k 4 u(t)= t²i - 8j + t³k r(t). u(t)= Is the result a vector-valued function? Explain. O Yes, the dot product is a vector-valued function. No, the dot product is a scalar-valued function.

Q: The compound interest formula states that if P dollars are invested at an annual interest rate of r,…

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A: Consider the functions 4)     f(x)=2x5)     f(x)=3x

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A: The given series is ∑i=1∞12i

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Q: 1 Find the linearization of the function f(x) = 5x+4 atz-1.

A: The given function fx=15x+4 at x=-1

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A: NOTE: Refresh your page if you can't see any equations. . . use the formula

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A: This question can be solved using the concept of partial derivatives.

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Q: T 45-50. Binomial series a. Find the first four nonzero terms of the binomial series centered at 0…

A: 49. The given function fx=1+x-23

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A: Given differential equation:- dNdt=N1-0.0008N , N(0)=1

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Q: 35a. Use long division to derive the first four non-zero terms of the Maclaurin Series for f(x) =…

A: The required Maclaurin Series for the function f(x)=tan x are: 1.  sin x=x-x33!+x55!-x77!+x99!-...…

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform.(Write your…

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A: laplace transform

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A: Given y=x3 x+y=30 and y=0

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Q: Q13) S 3+eZx dx

A: we can solve this as follows:

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A: Solution of given question is written in below steps.

Q: 7 Find f(x) if f'(x)= and f(1) = 4. X 7 --x-3+19 O B. f(x)= -28x-5 +32 7 O c. f(x)= 3 O A. f(x) =…

A: As we know the Power rule: ∫xndx=xn+1n+1+C ; n≠-1   Given: f'x=7x4 So, we can also write as;…

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A: Concept: The value of dz and ∆z is given by  dz=∂f∂xdx+∂f∂ydy∆z=f(x+∆x,y+∆y)-f(x,y) Here ∂f∂xand…

Q: did i type this in right?

A: Yes you need to type 3t2+6 in the box.

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A: NOTE: Refresh your page if you can't see any equations. . ...............(1)

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A: To write the limit representing  the derivative of f(x) at x=-3.

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A: Topic- Implicit differentiation

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A: To evaluate the value of given indefinite integral.

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A: NOTE: Refresh your page if you can't see any equations. . the given logistic function is

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A: NOTE: Refresh your page if you can't see any equations. . take natural logarithm on both sides

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A: We have to find the vertical asymptote.

Q: HOW YOUR CALCULATIONS 2. Do the following directions lie parallel to the plann? [211] ||(111)

A: Do the following direction lie parallel to the plane? [2 -1 -1]||(1 1 1)

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A: Given function, f(x,y)=8x2+xy-3y-6x+2.

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Q: b\ State and prove the theorem of these questions below, for each given functions find the value of…

A: answer is in next step.   as per guideline i can answer only one question .