01) Solve the differential equation with the given initial condition: y' - 6x²y + 4xy = y. where y(2) = 1

Q: Find T(t) and N(t) at the given point. (7) = N() = = T r(t) = 11 cos(t)i + 11 sin(t)j + tk; t = K|2

A: Given,…

Q: fand sketch it, for f(x, y) = x²

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Q: Find the limit of the trigonometric function. lim 9 sin(x)

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Q: d d Calculate[ri(t) r2(t)] and [r₁(t) × r₂(t)] first by differentiating dt dt the product directly…

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Q: 2. Show that F is a conservative vector field and then use that fact to evaluate SF. dr along the…

A: We need to show F is conservative vector field.

Q: nd the area between y = 8 sin x and y = = = 10 cos x over the interval

A: Topic:- application of integration

Q: Evaluate the following indefinite integrals using integration by trigonometric substitution.…

A: Solution in done in step 2

Q: y" + 6y' + 5y = 10sin (2x) A..! Inne(7)

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: = The Taylor series for f(x) = √2x − x² at a : 1 is Σ Cn (x - 1)”. n=0 Find the first few…

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Q: The heights h, and h₂ (in feet) above ground of two people in different seats on a Ferris wheel can…

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Q: 1 find the total differential dz. z=xsin y + x² z = (2x² + 3y)² z=5x-7y

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Q: Question 7 Given the function f(x) = 8 +5x², calculate the following values: f(a)= f(a+h)- =…

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Q: The graph of f(a) shifted right 3 units and shifted down 5 units. Of(r). 3-5 Of(x)= -3+5…

A: Let's find.

Q: A curve with polar equation represents a line. This line has a Cartesian equation of the form y = mx…

A: To write the given equation in the form of y  = mx + b.

Q: Find the limit. lim 1→2(t i - 5 j + t² k)

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Q: Find the exact length of the curve given by Length = x = 2t², y = (0 ≤ t ≤ 4).

A: A detailed solution is given below

Q: = fºx R/2 Given that evaluate - b² = g², use this result and the fact that 2 (6 cos(x) - 6x) dx. x…

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Q: (D² - D-2)y = cos x

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 2 Find az/ax if the equation yz - Inz = x + y

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Q: 2. Evaluate the following (Express all answer in Rectangular Form): d. √9+ 2i e. 2¹ + ln(2 + i)

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Q: Use Green's Theorem to evaluate the line integral ſ (y + e√x) dx + (2x + cos y²) dy, where the given…

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Q: Find the limit. Use l'Hospital's Rule wher lim [In(x⁹ – 1) – In(x³ – 1)] - - *-1*

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Q: Find the two x-intercepts of the function f and show that f'(x) = 0 at some point between the two…

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Q: Find . DO NOT SIMPLIFY YOUR ANSWERS. 1. log₂ √√2x² 2x² + y) + tan(x² − π²) = sin¯`¹²(x² − 1) + ½ /

A: To find dydx.log32x23+y+tanxπ-πy=sin-1x2-1+π2

Q: Find the arc length L of the graph of r(t). L = r(t) = 11 cos(t)i + 11 sin(t)j + tk, 0≤t≤ 2π

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Q: d Calculate =[rı(t) · r₂(t)] and [r₁(t) × r2(t)] first by differentiating dt the product directly…

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Q: Evaluate the integral 13 ƒ(x)dx geometrically for ƒ (x) = { |3 − x ; x ≤ 5 2; x > 5

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Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: Question 15 The cost, in dollars, to produce a designer dog leashes is C(z) - 8x +9, and the…

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Q: = Write the Taylor series for f(x) Find the first five coefficients. Co= C1= C2= C3= C4 e about x =…

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Q: Do as indicated. 2. Use the Squeeze Theorem lim sin (sinh x)csch x. x-18 to evaluate

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Q: Find the integral of the following equation integrate cos(x + pi/3) dx

A: Given problem:- Find the integral of the following equation integrate cos(x + pi/3) dx

Q: Σ(+6) της

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Q: Jc = − xj; P(−2, −4), Q(-2,-2)

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Q: x = 10t, y = t², (0 ≤ t ≤ 1). In each part, evaluate the line integral along C. NOTE: Enter the…

A: To find the values of given line integrals.

Q: 5x²³-4x²+3x LX Find the most general antiderivative of the function: f(x)=-

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Q: Solve for the solution: d3y/dx3 - d2y/dx2 -dy/dx +y = 0

A: Solution is given below:

Q: The force F (in pounds) on a person's back when he or she bends over at an angle from an upright…

A: The given model is: F=0.6W sinθ+90°sin(12°) where W represents weight of the person in pounds.

Q: II. Find an equation of the plane containing the points (0,2,-1) and (1,-1,-1) and perpendicular to…

A: we have to find the equation of plane.  Let, a,b c are the direction ratios of required plane 1.

Q: Homework 12 Polar: Problem 6 Find the area enclosed by one loop of the lemniscate with equation ² =…

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Q: Find the average value of on the interval [0,4]. favg f(x) = x²√√√17 + x³

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Q: Use the Root Test to determine the convergence or divergence of the given series or state that the…

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Q: 7. Find the slope of the tangent to the parametric curve x = t - lnt, y = t + lnt at the point (e +…

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Q: Find all solutions of the equation in the interval [0, 21). csc 0 7 3 If there is more than one…

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Q: d. Write the equations for any vertical asymptotes. e. What is the value of f"(x) on the interval -3…

A: We need to fill in the blanks.

Q: b Prove that: f(x) dx = F(x) =F(b)-F(a)

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Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

A: As per Bartley guidelines we are supposed to answer only three subparts of one question per post.…

Q: Find the derivative for each function. ㄷ 7. y=x² +2 9. y=2x²-x+3 A. 6. y=3x²-6 8. y=x²-3x+2 10.…

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