The given point is on the curve. Find the lines that are (a) tangent and (b) normal to the curve at the given point. 6x? + 4xy + 3y + 15y – 6 = 0, (– 1,0)

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A: Topic:- application of derivatives

Q: C., Given the graph of the function f(x) below. Determine the value of the following for each value ...

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Q: 13 The polynomial equation x4 - 6x3 + 10x2 + 2x - 15 = 0 has solution set _____. {3 + i, 2 - i, 3,...

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Q: 2п +1 E. Σ Зп +2 Е. n=0

A: The given data is: ∑n=0∞2n+13n+2  Solve using the integral test.

Q: х+ 3 f(x) %3D x2 - 9

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Q: А. Σ 5n –1 n=1

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A: For a quadratic equation:                                     ax2+bx+c=0 The solution is of this qua...

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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: The taylor series polynomial of f(x) at x=x0 is given by:                        f(x) = ∑r=0∞f(r)(x0...

Q: A curve has an equation of y = x - 24x2 +75. Find the point/s of inflection of the curve. О a. (2, 5...

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Q: The where c Is a constant, is equal toC 7. If y = 6e5, then y' = 30e*. The derivative of a product w...

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Q: 2п +1 Е. У Зп +2 n=0

A: ∑n=0∞2n+13n+2    Thus,  an=2n+13n+2    Thus, we can proceed further with ratio test

Q: u³ = a²t , find d’u %3D dt3 2a4 а. 9u5 10a6 27u8 -10a6 С. Zu® 40a6 d. U8 b.

A: A detailed solution is given below

Q: y'=2+ye^(xy)/2y-xe^(xy) find the exact equation

A: Exact DE

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A: answer is D a polynomial function is always differentiable. this is the property of simple function ...

Q: Find limit lim (x,y) -> (2,0)   ((Sqrt(2x-y)-2))/(2x-y-4)

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Q: Given the below differential equation, solve for the value of y(t) att = 3.8 s. 2.5y" + 11.2y' + 5.4...

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Q: Find T(t), Ñ(t), B(t), and curvature k for the following curve. (The curvature is constant.) 7(t) = ...

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Q: The graph of an exponential function is shown in the figure below. The horizontal asymptote is shown...

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Q: evaluate the differential equation: -5y +4y =z-2+

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Q: Find differential of the function ? = (x^2+2)^3 dy = ____ dx. When x = 4 and dx = 0.05, compute th...

A: We will differentiate the function Y=(x^2+2)^3 as follows 

Q: 1 The range of the graph y = sinx - 2 is _____. 2 ≤ y ≤ -2 -3 ≤ y ≤ -1 0 ≤ y ≤ 2 -1 ≤ y ≤ 1

A: We know that, -1 ≤ sinx ≤ 1 for all real x  

Q: Find the exact length of the curve. 2 3/2 y = = 12, 0<xs 1

A: Given ,y=23x32Aim: To find length of curve in [0,1]We know that L=∫ab1+[f'(x)]2dxTherefore,L=∫011+dd...

Q: Period: f(x) Vertical Shift: Horizontal Shift_ Start: End: Increments:

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Q: Rotate the axes so that the new equation contains no xy-term. Analyze the graph the new equation

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Q: point =)=at x = 2 -5 at x = -2 x² +1

A: Solving

Q: Evaluate the following integral. 6w + 4w - 54w° - 114w – 54 dw w° - 9w 6w + 4w – 54w° - 114w – 54 3-...

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Q: Given the function y = x* e* , find dty dx for x = -1. %3D

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Q: Find the solution of the differential equation that satisfies the given initial condition. dp/dt = ...

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Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If it d...

A: ∫210   6dx/(x-4)2 [-6(x-4)-1 ]102 [-6/(x-4)]102 -6/(10-4) +6/(2-4) -6/6 +6/(-2) -1-3 ∫210   6dx/(x-4...

Q: Rewrite each equation as requested. (a) Rewrite as an exponential equation. Inx = 4 (b) Rewrite as a...

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Q: cos4x - sin4x = cos 2 x 2 cos 2 x -cos 2 x

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Q: Compute the work done by the vector field F(x, y) = (ry, x² + y³) when moving a particle counter-clo...

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Q: Set up (Do not Solvel) the volume of the sold whose base is bounded by the graphs of yx+1 and y x?. ...

A: Given y=x-1y=x2-1The cross section are perpendicular to the x -axis are equalatral triangles a=x-1-x...

Q: Use logarithmic differentiation to find the derivative of the function. х — 5 y = x° + 5

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Q: 30 Choose the best answer: tan x + cot x =

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Q: 6. Find the exact solution of each equation, no decimals. Do not use a calculator and find the domai...

A: Given problem:-

Q: using laplare definstui fud

A: Find the Laplace transform

Q: Which of the following functions is differentiable for all values of x? a. flx) = 2r° + 5x? b. f(x) ...

A: Function which is differentiable for every value of x is

Q: Simplify to the form x + iy: (1 + i*sqrt(3))^13

A: Simplify to the form x + iy (1 + i3)^13 (1 + i3)2 = 1+23i-3 = -2 + 23i (1 + i3)3 = -2 -6 = -8 (1 + i...

Q: Q1 Choose only two: x+5 12+3x - 2. VI

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Q: dy Find by implicit differentiation. dx 7x2 + 3xy – y? = 9 dy dx

A: Differentiation of the above function is

Q: sec°xtanxdx

A: We need to evaluate :

Q: Find the equation of the sphere in standard form that satisfies the given conditions. center C(−1, 5...

A: Given, Centre =C(-1,5,4) And Radius , R=4  

Q: 31. /| z sin(z + y) dA, R= [0, #/6] × [0, 1/3] R

A: ∬ x sin(x+y) dA,R =[0, π6]×[0, π3]0≤x≤π6,  0≤y≤π3  

Q: 11/4 x  2 2/5 ÷ (11/4 + 21/12)  =

A: Given 11/4 x  2 2/5 ÷ (11/4 + 21/12)

Q: Let 8 be a twice-differentiable function with g'(x) > 0 and g"(x) > 0 for all real numbers x, such t...

A: We have to find g(6) 

Q: y'=(x^2+y^2)/xy solve using homogeneous equation (diff eq)

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Q: - 3x + y = 6 ax + 2y = 4 In the system of equations above, a is a constant. For which of the followi...

A: Given :-3x+y=6ax+2y=4

Q: Evaluate the flux (F*n)d-sigma where F = (3xy^2, 3x^2y, z^3) and M is the surface of the sphere of r...

A: We have to find the flux (F*n)d-sigma where F = (3xy^2, 3x^2y, z^3) and M is the surface of the sphe...