Use the formula k(t): |r'(t) × r"(t)|| to find k(t). r(t) = ti + t°j K(t) =

Q: Q1: Find dy/dx for the following functions:- (1) e – 3* = x sinh y (2) tan-12 = (Inx' + y²)

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Q: (7 cos° t dt 2

A: ∫0π/2 cos9tdt ∫0π/2 cost(1-sin2t )4dt here lets substitute that sint = u du/dt = cost du = costdt…

Q: QI: Find dyldx for the following functions:- (3) y = (tan x)tnz+ t (4) y = sin-(x² +x) + 5" %3D

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Q: Describe the graph of the equation. = 6 cos t i + 2 sin t j -k O Itis an ellipse in the z = -1…

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Q: 3. a) Determine the slope of the function, h(x) = 4sinx at x =". b) Find the slope of the line that…

A: We can solve as follows

Q: Determine if the following function is continuous or discontinuous at x = 0? 4z +5 f(2) = %3D 9- 32

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Q: Use trigonometric identities to transform the left side of the equation into the right side (0 < 0 <…

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Q: valuate the integral by interpreting it in terms of areas. In other words, draw a picture of the…

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Q: e cosx sin x dx 1-e2 cosx

A: Given problem:-

Q: Suppose a certain baseball diamond is a square 90 feet on a side. The pitching rubber is located…

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Q: Consider the initial-value problem y" + 4y = 5 sin 3t, y(0) = 0, y' (0) = 3. %3D (a) Use the Laplace…

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Q: In(x) -dr

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Q: for the N(0) is it 0k? or can I write it just k?

A: Yes, N0=-12i+12j+0k.

Q: 15 of 20 -722 –8x =? limz→00 3–72²+6x+6 O Does not exist O 00 O 7

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Q: c). Using an integrating factor solve the equation dy + 2y/x = x dx

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Q: For what values of a and b is the line-5x +y b tangent to the curve y = ax when x = 37 a = b D %3D…

A: -5x +y  =b    and curve is y = ax3 at x =3 here for tangent the slope of curve and line is same…

Q: Show that the function f defined by 1, (x, y) = (1, – 1) f (x, y) : .2 x + y (x, y) # (1, – 1) x + y…

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Q: You are given a task to find a series expansion about x = 0 for a solution to (x – 1)y" – a²y' + y =…

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Q: Determine the vector field of F. F(x, y) = 9i – 3j %3D

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Q: Question 3 Suppose C=0, so that 2y 24y 5x3 = 0. Find all points (x,y) at which the tangent line to…

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Q: х- у 3. f(x, y, z) = y? + а. f(3, —1, 2) b. d. f(2, 2, 100) с.

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Q: Use the chain rule to find and , where as z = x² + xy + y, x = 6s + 9t, y = 5s + 8t %D First the…

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Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of f(x) = t3+3°dt f'(x) =…

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Q: Find the slope of the tangent line to the parametric equations: x = 3t2 - 3, y = 2t + 1 at t = 1. %D…

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Q: Apply

A: We will solve the integration.

Q: ||r(t) × r"(t)|| ||r(t)||° Use the formula k(t) to find k(t). 13 9ts r(t) = e"i+etj K(t) :

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Q: Find curl (3zi + 4xj+ 5yk). curl(3z i+ 4xj+ 5yk) = ( i )i + ( i )j + ( i )k

A: We will find the curl.

Q: Evaluate the line integral, where C is the given curve. xy ds, C: x = t2, y = 2t, 0sts 3

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Q: The point is on the terminal side of an angle in standard position. Find the exact values of the six…

A: Given that the point is on the terminal side of an angle in standard position. To find the exact…

Q: Answer the question in FULL details. Show ALL your steps and work in your calculations. Answer in…

A: A) y=3x^2+3x B) y=(e3x+e-3x)/2 C) y=log5(tanx).

Q: 7. Given that tan (A) = and angle A is in 3rd quadrant and cos(B) = – - and %3D 13 angle B is in 2th…

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Q: Q1) Determine if the following integrals converge or diverge. If the integral converges determine…

A: Given query is to find integral converges or diverges.

Q: x+1 8. -dx (x-1)

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: 7. Interpretations of Inter a) Determine the position function, s(t), of an object if the…

A: a)

Q: V11 T Use the information given about the angle 0, sin 0 = 4. <0<n, to find the exact values of the…

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Q: e product (4 8 10 9)(2 7 6 11)(1 35 12)

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Q: Factor the expression. Use the fundamental identities to simplify, if necessary. (There is more than…

A: Given problem:- Factor the expression 1-2cos2(x)+cos4(x)

Q: Use the properties of summation and the Summation Formulas Theorem to evaluate the sum. Use the…

A: Summation Thorem formula states that               ∑i=1ni=nn+12

Q: If fex) x2 f'co) 19+ t? dt find f'c3) %3D

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Q: Find r'(t). r(t) = (tan-'(9t))i+t cos(t)j – Vēk NOTE: Enter your answer in terms of i, j, and k.…

A: We can solve this as follows:

Q: 7. Given that tan (A) = - and angle A is in 3rd quadrant and cos(B) = - and 13 angle B is in 2th…

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Q: (8x + 4x)v4x² + 8 – 24x³ – 32x If f(x) = (/4x2 + 8 - x*) then f'(x) = 4r2 +8

A: f(x) = (4x2 +8 - x2 )2 f'(x) = (24x2 +8 - 2x2)(8x/(24x2 +8)  -2x ) f'(x) = ((24x2 +8 - 2x2)(4x -…

Q: dx 5-x?

A: We will solve the integral.

Q: -24 e 5n costx dy Ln(sinx) dx

A: To solve the following problem

Q: A chain saw requires 2 hours of assembly and a wood chipper 5 hours. A maximum of 30 hours of…

A: We have to find the number of chain saws X and the wood chippers Y to maximize the profit P(X,…

Q: A certain substitution gives S sin³ x cos" x dx = S(u7 – u5) du. What is n?

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Q: dy Find of sin x + cos y = ety. dx

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Q: Consider the exact first order diff. equ: M(x, y) = 2.xy – 3x? N(x, y) = x² - 2y (I): (2xy – 3x )dx…

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Q: cy?t1) e COSX y2 dy 8- COSX CotX

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Q: 8 tan¬1 n 1 + n² 00

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