Given the equation 5 sin 6xy = 3, evaluate dy Assume that the equation implicitly defines y as a differentiable function of x

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A: The objective of the question is determine the length of the given curve.

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A: We have to calculate the least squares line.

Q: What is f'(x) given the integral function •5x+1 f(x) = 5x+¹ cos(e") du? ○ f'(x) = 5 cos (es) o f'(x)…

A: We have to find out derivative

Q: 5. What is the equation of the asymptotes of the hyperbola defined by x²-4y² + 4x + 40y - 92 = 0

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Q: find the limit, if it exists. If the limit does not exist, explain why. limx→2 1−|x|^2/1−x^2

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A: Accerelation vector  a(t)= 6i +9k  v(0)=3j and r(0)=0  Find  Velocity, position vector .

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A: Follow the procedure given below.

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A: Given :fx=1x

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A: Given :∫csc4x+cot4x2dx

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A: This question is based on double integration.

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Q: 3. 1 S [(2x - 4y)dydx 31 1 -1

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Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = t³i +…

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Q: xdx

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Q: cos-¹ Q6A)If y cos = prove Zyy + z = 0. B) Z = (1 + i)(2-1)-¹, find |21. 倉

A: Simplify given equation in z then  two times partially differentiate z

Q: H.W: Evaluate the integral (x²y - 2xy) dydx 1. 30 0-2

A: As per your query the solution of the question no 1 is given in the next step.

Q: 1. Solve the following a) 430.00(1+0.05) b) 1.2:4.2:60= 5 45 4 64 c) y: 9 8 (1+0.05)³3 -1 0.05

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Q: Find the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about x= xo and then find the nth Taylor…

A: Taylor series of function fx at a is defined as:…

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Q: Find the characteristic equation, the eigenvalues, and bases for the eigenspaces of the following…

A: I am attaching image so that you understand each and every step.

Q: Consider the three matrices A = (b) 2 -1 1 0 -1 2 94-1 B = 2 y and C = −1 multiplication is…

A: The objective of the question is determine sizes if possible and evaluate the values x,y and z.

Q: 1.4 Assuming that C₁ Cos (wot) and C₂ Sin (wot) in 1.2 are two independent solutions of the SHO…

A: It is given that C1 Cos( W0t) and C2 Sin(W0t) are two independent solution of the SHO differential…

Q: Find the arc length of the graph of the function over the given interval. y = In x, [1, 8] Step 1…

A: topic- arc length of a curve

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Q: If the L[ eatsin3t ] = a/( s² + bs + 42), determine the value of b.

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Q: Find the curvature K of the curve, where s is the arc length parameter. r(s) = (1 + s)i + j K = (No…

A: The given problem is solved below in detail.

Q: 2 The function f(x) ==, x0, is one-to-one. X Find an equation for f(x), the inverse function. ...…

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Q: Find the indefinite integral. x + 7 x² + 14x5 Step 1 To find the indefinite integral dx J 1 x + 7 x²…

A: To find the value of given indefinite integral.

Q: Step 2 Use the following trigonometric substitution. x = tan (0) tan (0) Differentiate with respect…

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Q: Q5/ Find the area of the region enclosed by the curve y² - 4x = 4 and the line 4x - y = 16. 3,6 16…

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Q: As per the trigonometric substitution x = sin(0), the following triangle is obtained. cos(0) Submit…

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Q: Find the derivative. G(t) = sinh(ln(t))

A: Topic = Derivative

Q: Given f(x) = 3x² Rn = 6, find a formula for Rn on the interval [2, 5]

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Q: 2. At a local maximum point f '(x) = 0. a) always b) sometimes 3. If f '(x) = 0, then the point (x,…

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Q: Write the sum in sigma notation 52 +55 +58 +61 +...+ 145 A ΣΒ j=1 A= B= Hint: The answer for A…

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Q: x+2 3.) (x²-1)(x²+1)² of factor. dx; Solve by using partial fraction. Indicate the type

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Q: Use the half angle identity for sin² x. sin²(x) Hence, sin² x = ~ √₁² (₁²- V = π (1-sin²(x) 2 sin 2x…

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

Q: lim h→0 (e) cos( 4 + h) - 1 h

A: To find the limit of following function

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Q: 2 Matrix A = · (2 ²]‚B = [† __²₂], find AB . Solve differential equation d = -(2ln5y+x¹) dx 2xy-1

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Q: 6. f(8x³ - 6x² + 12x −9)dx

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Q: Consider the given function, h(x) = -x² +6x-13. (a) State whether the graph of the parabola opens…

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