b. Find the unit tangent vector and the principal unit normal vector for motion R(t) = (cos 2t)i + (sin 2t)j %3D

Q: ne graph of y =- have a horizontal tangent line? +9

A:

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A: We will find the derivatives of the given function y=ecos2x in the following step.

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A:

Q: Find the arclength of y = 2x/2 3/2 on 1 < x < 3

A: We know that the arclength of a curve y=f(x) on a≤x≤b is given by L = ∫ab1+f'(x)2 dx

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A: To find the laplace transform of the folowing function.1+2tt

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A: We have to find the area of the shaded region of the figure given below.  Cleary the shaded region ...

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A:

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A:

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A: Given

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A:

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A:

Q: If f(x) = 7 cot-l+ 5, then find the value of f'(-6) is -5 37 -6 37 O 00 O 7 37 O -7 37

A: Topic:- application of derivatives

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A: Consider I=∫dx3+5 cos xwe use the formula cos x =1-tan2x21+tan2x2

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A:

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A: Write the formula for the surface area and volume and then apply total derivative. 

Q: The derivative of the function y = cot¬1(csc x) is: csc x cotx cSC X cot x y' y' = csc?x+1 csc?x+1 t...

A: See the details solution in below

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A: Given query is to find that differential equation is separable or not.

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A: Use differentiation for finding the slope.

Q: Sketch the region enclosed by y = 4x and y 4x2. Find the area of the region. %3D

A:

Q: S cos?x-ex

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A: Given: f(x) = (x - 2)2 What is the integral function g(x) that defines the area under this line betw...

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A:

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A: Given,           v=2i-j+3k , b=6i+6j+7kTo find : i The vector component of v along b.               ...

Q: Determine the Riemann sum that represents the illustration below. The function is lx) = 2x. Y 6. 4- ...

A: Explanation of the answer is as follows

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A:

Q: 13 Which of the following is true about f(x) = [x]? A. The function is continuous at x = 0. B. The f...

A:

Q: Find the minimum distance from the point to the plane x-y+z=3 at (1,-3,2)

A: We will find the minimum distance from the point to the plane x-y+z=3 at (1,-3,2) in the following s...

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A:

Q: If f(a) = 3 cot- * + 6, then find the value of f(-8) is -6 V65 V65 оо оо о

A: Solution ) f(x) = 3cot-1x + 6 Differentiate with respect to x  f'(x) = 3 (d/dx)  cot-1x + (d/dx) (6)...

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A:

Q: nsider the parallelepiped with adjacent edges u = 6i + 7j +k v = i+j+5k w = i+ 7j + 9k d the volume.

A:

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A: (6) (i) Here your first two examples are right. For the third example do it as:   Assume a three di...

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Q: dy Find using implicit differentiation, for the equation x + y³ = 9 is dx x2 y? x2 x2 No OO O

A:

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A:

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A: Given that:  C is the right triangle.  The triangle is isosceles.  Legs AC=BC=20.   Since it is an i...

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A:

Q: ( 2² – 2x + 1, æ < 2 13- a, a22 Evaluate the following limits for h(a) = and Justify your answer. ()...

A:

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Q: Verify that the given function u is harmonic in an appropriate domain D. Find v(x, y), the harmonic ...

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Q: 144. Identify the length of the curve y = x over the interval [2,6] 49

A:

Q: 17. If y = tx, where t is the parameter, what are the parametric equations of the curve x' + y' = 8?...

A: solution:-y=txx3+y3=8x3+tx3=8x31+t3=8x3=81+t3x=21+t33

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A:

Q: If f(x) 4 cot r + 10, then find the value of f'(-7) is O 4 50 4 50 10 50 V50 7,

A:

Q: Let a = ci +j and b = 4i + 32j. Find c so that a and b are orthogonal. C = i

A: Recall: If two vectors a and b are orthogonal then their dot product is zero that is a·b=0

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A: The given graph is f(x)=x2+1

Q: Rewrite the following integral using substitution: " s in3xdx

A: We can rewrite the integral using substitution as below.