Find an equation of the line tangent to the curve √xy+3y=200 at the point (1,64). An equation of the tangent line is.

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A: To evaluate  shown here.

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Q: Use the limit laws to evaluate lim (3x − 12)√√x + 4. x→6 Enter the exact answer. For example, enter…

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Q: 2. (a) Find the slope of the tangent line to the curve f(x) = 2x³ - 3x at x = -1 using a definition…

A: Note:As per our guidelines we are supposed to answer only one question if there are multiple…

Q: = f(x) dx (f). = [(x)6. (x) (p) = [((x)6)4] (ә) (c) ax (x") =

A: According to this question we have to solve parts d,e,f only.

Q: Find the exact length of the curve. 36y² = (x² - 4)³, 2≤x≤6, y 20

A: Find the exact length of the curve.36y2=(x2−4)3,2≤x≤6,y≥0

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Q: (a) Show using the product rule that [f(x) g(x)h(x)]' = f'(x)g(x)h(x) + f(x)g (x)h(x) +…

A: we are given a product of three functions and we need to find out the derivative using the product…

Q: by defintion the Laplace transform of a function f(t) is an improper integral of the form F(s) = √°*…

A: The definition of Laplace transform f(t) Given function

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Q: 4. §11.5. Q10. Use appropriate form of the chain rule to find dw/dt. w = √√√1 + x2yz¹x; x = ln t, y…

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Q: Find the length of the spiral r=0², 0≤0≤√21. The length of the spiral is (Simplify your

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Q: Find the area of the following region. The region common to the circles r = -8 sin 0 and r=4 The…

A: The region common to circles and

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Q: Solve the following differential equations using Exact method ху (2+ye Jdx + (x-2y) dy =0

A: we need to find out the solution of the exact differential equation.

Q: Use the properties of logarithms to expand the following logarithmic expression as much as possible.…

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Q: 3. $11.3. Q96. Given 2 (a). ປົນປີ10ນ 03 : (b). 01-0 (c).axay · 8 : (2 — y), find

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Q: Find dy dy dx by implicit differentiation. tan(x - y) = = y 7+x²

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Q: ind the curvature of the space curve. r(t)=-5i + (t+8)j + (In(cost)+1)

A: r(t)=-5i + (t+8)j + (In(cost)+1)kTo find:Curvature of the sapce curve

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A: The linearity property of Inverse Laplace Transform:Where  and  is the constant.And the Inverse…

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A: Since you have posted multiple questions, we will provide the solution only to the first question as…

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Q: 7. The arch of an underpass is a semi-ellipse10 meters wide and 4 meters high. Find the clearance at…

A: We solve the given problem by using the concept of the ellipse.

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Q: Find the arc length function for the curve y = 2x3/2 with starting point Po(16, 128) s(x) = ||

A: The given function is,The given point is,The lower limit of x is  and the upper limit is

Q: Each of two tangents to the circle x² + y² = 25 has a slope 2. Find the points of contact.

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Q: Given that f(3) = 2, f'(3) = 5, g(x) h(x) = f(x), then find g'(3), and h'(3) = f(x)

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Q: Find the total differential d2 for the dx = 0.01 X= 2 Y = 0 and dy = 0.01 J2 and 42 LE of function…

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Q: 9. Assume that the oil spilled from a ruptured tanker spreads in a circular pattern (A = πr²) whose…

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Q: Write an equation for a line parallel to y - y = 2x 3 and passing through the point (2,0)

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Q: (0) dx (logax) = (q). (sin-¹x) = dx (p) & (a*) = (r) dx (tan-¹ x) =

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Q: ex - 32 √x +x 22

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