Find the slope of the tangent line to r²e³ + y²e² = 2e at (1,1).

Q: Q1:Discussion a continuity of the function f(x, y) at the point (0,0), where ey sinx f(x, y) = X (x,…

A: We want to check the continuity of the function at (0,0)

Q: tan² y = x (By implicit differentiation)

A: The given equation is tan2y=x.

Q: Question 14 A 60-m climbing rope is hanging over the side of a tall cliff. How much work is…

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Q: 2. Find the solution of the differential equation ₂ dy 2x² = dx 3xy + y². which satisfy an initial…

A: Solved below.

Q: Problem r7 ¯7² xVx² - xVx² 0 + 1 dx

A: Topic:- application of integration

Q: What is the particular I solution of the differential equation (2x + y²) dx + 2xydy = 0 when x = 1…

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Q: 9. y = 3 Arcsec 3x

A: On solving this we will get

Q: 9. Find the interval of convergence of the series n=1 5" (x-3)" √√n

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Q: dw Q11- express by using the chain rule: dt w = ln(x² + y² + z²) x = cost, y = sint, z = 4√t

A: We have to express dwdtby using the chain rule:

Q: Given cost and price (demand) functions C(q) = 100q+43,000 and p(q) = -2q + 890, what profit can the…

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Q: Find the exact value of the surface area generated by revolving the curve 1 + 1≤x≤2, about the…

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Q: A region is bounded by the y=x² and y=6x-x² Which of the following integrals would approximate the…

A: We can solve this as follows:

Q: Differentiate f(x) = tan¯¹(3x). Use exact values. f'(x) =

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Q: dy Use implicit differentiation to determine given the equation x² + y² = 9. d.x dy dx =

A: In implicit differentiation, we differentiate each side of an equation with two variables (usually x…

Q: The degree of DE: (y")^2 +3y(y')+y^3 (y')^5 = 5x 02 01 05 0 3

A: Recall:  The degree of D.E. is the highest power of the highest order derivative in a D.E.

Q: x³ + 3y = xy (By implicit differentiation)

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Q: Solve the D.E XỲ+Y=- 1 y2

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Q: Find the line integrals of F = 4yi + xj + zk from (0,0,0) to (1,1,1) over each of the following…

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Q: FCILICI. B. Find the general solution of the following 2nd order differential equation: y +2y + 2y =…

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Q: Suppose a population of fruit flies changes at a rate of g(t) = -3e0.01, in flies per day. If the…

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Q: The graph of y = f(x) is given. 5 4 1 -4-3-2-1 123 -1 324 2 2 -5 -6+ State the value of each limit,…

A: Consider

Q: (d) Find a vector function that represents the curve of intersection of the two surfaces: the xy…

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Q: Home work: 1. 3. 5. 7. 9. 11. [xsin / dx [₁² t² cost dt x ln x dx -1 tan y dy x sec² x dx S [xse…

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Q: 2 Find all local extreme values of f(x) = -2.3 + 11x² 56x + 30. 3 The FIRST local extreme value,…

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Q: Find the slope of the line satisfying the conditions. parallel to 7x + 5y = 57 Select one: O A. m m=…

A: We know  slope of two parallel lines are same. Now,  the given equation of line is 7x+5y =57. We…

Q: (c) Express the number 1.234567 as a fraction (in its simplest form) using the sum of a geometric…

A: Ans=45679/37000 For detail...go through the solution.....I have solved step by step in detail

Q: Evaluate (x²sin y-xcos(y)) dy A x²(1+ sin(1))-xcos (1) + C B x²(1-cos(1))-xsin (1) + C C 2sin…

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Q: What integration technique can be used to integrate: 5√3+x² dx X

A: Follow the procedure given below.

Q: Q1:Discussion a continuity of the function f(x,y) sin x (x, y) = (0,0) f(x, y) = x (x, y) = (0,0)…

A: To find whether given function is continuous at (0,0) or not.

Q: If an object is dropped from a 150-foot-high building, its position (in feet above the ground) is…

A: Negative sign of the velocity is due to the downward movement of the body.

Q: Problem x√x+1 dr

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Q: In Exercises 1 and 2, compute the solution of the given IVP. 1. d²y dt2 +9y2 cos(3), 2 cos(3t),…

A: Since you are asking multiple questions. We are answering only the first question as per our…

Q: y = (4 + ³√/x)³ 3

A: Inverse function

Q: Let f(x) = 2x³ - 3x² - 120x+7. a. Find all points on the graph of f(x) at which the tangent line is…

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Q: 10. At what rate is the vertex angle of a right circular cone changing when the radius is 3 ft and…

A: The given problem is solved below in detail.

Q: Using Fundamental Theorem of Calculus (FTC). Compute the following

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Q: Arrange the choices in order 1,2,3.. to prove: For any sets A, B and C x (BU C) = (A x B) U (A x C),…

A: Here we have to arrange the option.

Q: 2. (y - x + xycot x) dx + xdy = 0

A: We have to solve the given differential equation.

Q: 2 9- r2-x Consider the integral fff dv = [₁² f³-²³² ²6²² + . dz dy dx. 0 S (a) Sketch the solid S.…

A: Let's solve.

Q: 19 A curve with polar equation r = 8 sin 0+17 cos 0 represents a line. This line has a Cartesian…

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Q: -0.5 3. f5 x(1-x)³ dx 0

A: To evaluate the given definite integral by using substitution rule.∫00.5x1-x3 dx

Q: 3. Use the given graphs to sketch the graph of f(x) + g(x). Explain your process. [A3] [C2] fox)…

A: We have to solve and draw the graph.

Q: Find the absolute extrema of f(x) = x³ - 6x - 1 on the interval [-2,3].

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Q: Q2: test if (AB)¹ = B¹A¹ A = 4 1 4 -3 61-63 0 2 B = 0 2 L3 5.

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Q: dy Q1: Find the for the following functions: dx 1- y = e(x+ln 5x) 2- y cosh-¹ sin 2x -1 3- y = asinh…

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Q: Let f(x) = 2x³-9x² - 24x+2. a. Find all points on the graph of f(x) at which the tangent line is…

A: Topic = Derivative

Q: Using Cramer's Rule to solve (if possible) the system of linear equations 1 A -10 1 B 11 N SSSUSU…

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Q: 3. 4. If = (-12, 4, 8) the position vector of u is...........

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Q: What integration technique can be used to integrate: A Trigonometric Substitution B Integration…

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Q: 03: Fill in the blanks in the following: 1. If a (3,-2, 6) and b=(4,-1,-6) the axb = ******** .

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