Find the equation of the tangent plane to the surface f(x,y)=In(4x²-2xy-y²) at the point P(-1,-1,0).

Q: . y = x2 and x2 = y

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

Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

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Q: 2. a) Calculate the 4th roots of (5 - j3) b) Differentiate the following functions clearly showing…

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Q: Find the general antiderivative of f (x) = 4 x ln x²

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Q: Consider the vector-valued function R(t) = {{ (a) Find the domain of R. (b) Show that is continuous…

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Q: min

A: Please refer to the image below

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A: Given function, f(x)=1.6x+8.3 Where x is in months.

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Q: Set up the definite integral required to find the area of the region between the graph of y = 12 -…

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Q: Find the points on the cardioid r = sin(2θ) where the tangent line is horizontal. Draw.

A: We have to draw the cardioid r=sin(2 theta)  And find the point where the tangent line is…

Q: [u udv-uv- - [vdu to Explain why the substitutions below are inappropriate. Let dv =x dx 1. Suppose…

A: This questions uses ILATE  rule

Q: (a) Assume that f(x) is a function defined by f(x) = x²-3x+1 2x - 1 for 2 ≤ x ≤ 3. Prove that f(x)…

A: Given.

Q: The function f(x) = 7 1+9x² f(x) = Σ cnan. n=0 Find the first few coefficients in the power corios…

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Q: 5. If f f(x) dx = 12 and f f(x) dx = 4, then all of the following must be true a. f f(x) dx = 16 ✓…

A: topic- definite integral

Q: Q) find differential equation of the following equation 1) y' = y-x y+x

A: Solution of the above differential equation is

Q: (5) Σ.1 η=1 η! 102n-1

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Q: . What is the snortest distance between the parabola y=2x² and the line y=4x-4

A: Shortest distance between two curves are always along the common normal.

Q: The surface of the sun has dark areas known as sunspots that are cooler than the rest of the sun’s…

A: As per guidelines, we are going to solve only one problem. So please repost the other problems…

Q: 5. Find the volume of the solid in the first octant bounded by the two cylinders x²+y²=4 and…

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

Q: problem: Find the vector below. ting the unit normal vector of A = 40 + 7 ₁ 0 - 3 K

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Q: sider the function p 3 of 3: Find lim f(x). x--6 f(x) = = lim f(x) x--6 Sx² + 12x + 22 19x + 100 if…

A: Topic:- limit and continuity

Q: Q) find differential equation of the following equation (1 + x²) dy + (y - tan-¹(x))dx = 0

A: On solving this we will get

Q: A gas station stores its gasoline in a tank under the ground. The tank is a cylinder lying…

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

Q: Question 10 Find the general antiderivative of f(x) = O2 In|ln 2x + C 1 + C 2 In 2x Olnln 2x + C + C…

A: The objective is to find the general antiderivative.

Q: Consider the differential equation y' = y² where y is considered to be a function of . 1 In this…

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Q: 1. Given f(x)=x+5 and g(x)=x²+8x+15 Sketch the graph of y=- _f(x) g(x) Mark the asymptote(s),…

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Q: √√(x + y + 2) ds, 0sus 5, 0≤v≤1 S is the parallelogram with parametric equations x = u + v, y = u -…

A: Solution is here

Q: c) A loan of $A is made on 20 April 2015 at a simple interest rate of 6% per annum. The accumulated…

A: Please refer to the image below

Q: 5. 6. (log4(x²) dx x (log4 x)² ORA dx

A: We have to evaluate integral

Q: 2- 3- Evaluate the integrals in Exercises [² dx L₁3 3 dx 3x - 2 dy 1- 2. S sec y tan y 2 + secy

A: We can answer all the three questions as below.

Q: Given triangle ABC, A = 40, a = 15, and b = 19, find B to the nearest degree. Do not round answers…

A: Given triangle ABC, A = 40, a = 15, and b = 19 To find B to the nearest degree.

Q: II. (3 + x, if x ≤ 1 (3-x, if x > 1 Sketch the graph of the given function. 6. Let f(x) Investigate…

A: we have to check continuity at x=1 for the given function

Q: Integrate (three) of th 1) f sin6x cos3x dx 4) [x² (1+¹)4 dx

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Q: 5 -5 g(x) dx

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Q: S₁ √√x² √√√xª dx 4 -2

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Q: Sketch the region bounded by the given lines and curves. Then express the region's area as an…

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Q: find differential equation of the following equation 2) (1 + x²)dy + (y-tan ¹(x))dx=0

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Define a vector field on the plane as follows: F(x, y) = (x + y², e³ + 6xy). Let C be the square…

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Q: 2 problem: it | b₂ b3 2 LG C₂ Cz 201-2 b b 2 46 40 2 5 - 203 bz 3 403

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Q: (b) Prove that the improper integral ]] converges. dr dy (1 + x² + y²)³/2

A: Given problem:-

Q: tid Q3. Evaluate the following integrals 1) cothx.csch2x. dx (50-3x - √x+1+73 44x

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Q: What is the equation of the given ellipse? Y (-3, 2) (-1,-1.5) X

A: Graph of the ellipse is given, we have to find its equation.

Q: Evaluate the difference quotient f(a+h)-f(a) for the function f(x) = x² + 4x - 5. h 2a +h+4 h+4 2a +…

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Q: 3. Evaluate 5 sin rdx B

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Q: 1. Find the indicated limit 1- cost, (a) R(t) t 1+ cost, i+ (b) R(t) 1-sint = = -i+e¹j+ek; lim R(t)…

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Q: What is the average rate of change of f(x) from x₁ = -8.2 to x₂ = 2.8? Please write your answer…

A: Follow the procedure given below.

Q: Find dy/dx of the following: a. y=sinh-'5x b. y=sinh- c. y = cosh¹ √x

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