Let f(x) = Then f'(x) = π The equation of the tangent line to y = f(x) at a = can be written in the form y = mx + b where 4 m= 4 sin x 2 sin x + 6 cos x b= 2/3 2 1+√3 X X and

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Q: c) On the cartesian plane below, put a point where the following coordinates are. a) A (-5, 4) m i…

A: Consider the figure

Q: Evaluate the following integral using trigonometric substitution. x² √√64-x² S dx

A: I=∫x264−x2dx

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Q: Find the vertex, focus, and directrix of the parabola, and sketch its graph. (x - 6)2 = 2(y + 4) = 0…

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Q: Find the domain of the function. h(u, v) = √3-u² - v² Ou+v≤3 Ou² + v² 0 Ou+v<3

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Q: (a) In(2x + 1) + In(10) = In(50) (b) (c) log(9x + 1) = 2 e2x - 3ex + 2 = 0

A: Given equations to solve for 'x'

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A: The equation  defines a curve named as the Folium of Descartes.By using implicit differentiation to…

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Q: Determine whether the Mean Value Theorem can be applied to f on the closed interval [a, b]. If the…

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Q: What is the center of the sphere given by the equation x² - · 6x + y² – 2y + z² +82 +17 = 0? -…

A: The standard equation of a sphere is given by  where (h,k,l) is the center of the sphere and r is…

Q: 1) State the order of the given ordinary differential equation. Determine whether the equation is…

A: To determine the given equation is linear or non linear.

Q: Find the absolute maximum and absolute minimum of the following function on the given interval. ƒ(x)…

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Q: Describe the x-values at which f is differentiable. (Enter your answer using interval notation.) X…

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Q: For the given double integral, sketch the region of integration and write an equivalent double…

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Q: Find the maximum and minimum values of f(x, y) = xy on the ellipse 5x² + y² = 4. √20 maximum value…

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Q: Sketch the region of integration, reverse the order of integration, and evaluate the integral. dy dx…

A: To find:-

Q: ∞ Σ7(-0.8) is an alternating geometric series, which k=0 diverges converges. Σ7(-0.8) k - k=0 Enter…

A: To determine whether the alternating geometric series diverges or converges.

Q: LET • (CX)= In [x²(x+5) ³ (x² + 4)⁰7 f'(x) = LET F(x) = \n [X²(X + 3) ³ (X² + 2)²] Cico

A:

Q: (2) Solve the given homogeneous equation by the appropriate substitution y dx (x + y) dy = 0. - You…

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Q: Find the volume of the region in the first octant bounded by the coordinate planes, the plane x+y=5,…

A: Equation of plane : and equation of cylinder : Find the volume of the region in the first octant…

Q: Solve the given initial-value problem. Y(x) = y" + 4y' + 5y = 35e-4x, y(0) = -5, y'(0) = 1

A: y'(0)=1

Q: Consider h(z): 2 5 - Oh is concave down on: Oh is concave down nowhere. 1 2 Determine the intervals…

A: Consider the function To determine the intervals on which  is concave up and concave down.To…

Q: If what are the bounds of integration for the first integral? a= 11 [ f(a)d= = [ f(x) dx + " f dx […

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Q: Sketch the region enclosed by y = 7x and y = 8x². Decide whether to integrate with respect to x or…

A: In this question, we will find the area of the region.

Q: Use the second degree Taylor polynomial for x at x = 8 to estimate 10. Round your answer to four…

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Q: 1. Using the fundamental theorem of calculus part 1, along with properties of the definite integral…

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Q: 1) State the order of the given ordinary differential equation. Determine whether the equation is…

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Q: The function f (x, y) = x³ - 3x² y + 3xy²-y3-11 22-2xy +49 y2 - 16 x + 208 y + 131 has a critical…

A: In this question, we will solve the all parts.

Q: Sketch the region of integration, reverse the order of integration, and evaluate the integral. }} dy…

A: To find:-

Q: Solve the given boundary-value problem. y-10y+25y=0, y(0)=1 y(1)=0

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Q: 3 Use algebra to find the point at which the line f(x) T- 4 59 6 h(x)= - Y 4 3 C Write the values of…

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A: Consider the following.To eliminate the parameter to find a Cartesian equation of the curve.

Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A: r=6cos⁡(θ),θ=π3

Q: 5 Determine the difference quotient for the function f(x) = 2x-1.

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Q: A projectile is fired with an initial speed of 240 m/s and angle of elevation 60°. The projectile is…

A: The initial speed of the projectile isAngle of projection, The initial vertical position, The…

Q: Find d'y if (x)=3x³ (√x-2). d³y dx³

A: To find Note: Since the student has posted multiple questions and does not mention any specific…

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Q: Find the derivative b. y= sec^-1(2x+1) c. y=x^e^x

A: I have appended the formula used in the solution procedure.

Q: For the vectors u = 3ỉ − 8j + 2k and - v = 4i - 2j – 4k we have - ü × v = 28i + 20j +38k. Select…

A: The given vectors

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Q: ketch the region of integration, reverse the order of integration, and evaluate the integral. 10 10…

A: First sketch the curve by use of the limit of integration.

Q: Consider the function f(x, y) = (4x-x²) (2y - y²). Find and classify all critical points of the…

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Q: Let 16x-5 1x² +5 Enter the exact value of the one-sided limit lim f(x) 3-2 f(x) = if x ≤ 2 if x > 2

A: