7x° + 8x Let f(x) Find F(x), - x3 where F(x) is the antiderivative of f(x) that passes through the point (1, 5). Round to 4 decimal places if necessary.

Q: What is the direction in which the function f(x, y) = yx - increases most rapidly at the point (-2,…

A: Given: f(x,t)=yx2-x/y2      at (-2,1)

Q: 2) y^2 = 4x, x^2 = 4y; revolving around the x-axis. Use washer method.

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Q: Find the linear approximation to the equation f(x, y) = 5 ln (x* – y) at the point (1,0,0), and use…

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Q: Solve the problem. Find all points on the curve y = cos x, 0 sxs 2T, where the tangent line is…

A: The given curve is y=cos xFind all points on the curve y=cos x , 0≤x≤2π , wherethe tangent line is…

Q: Find the approximate change in z when the point (x, y) changes from (9, 0) to (9.03, 0.03). f(x, y)…

A: Given function is: z=fx,y=7xe-y  To find the approximate change in z when the point (x,y) changes…

Q: c. f(1) d. Is f differentiable at x = 3?

A: Given The graph of function f as  To find: c. f1d. is f differentiable at x=3?

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Q: f(x) = Vxdx 0. 1. Trapezoidal Rule

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Q: 3y + 2y Solving by variation of parameter y" Wronskian W is: 3e*cosx, the value of |

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Q: Q.1 The natural domain of function f(x, y) =+ Vx²y³ is %3D lyl

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Q: e the following nth-order equation using the variation of parameter method: y"-3y"+3y'-y=

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Q: / Find the value of the Constant a& b such thet X > 2 fex)=} ax +b iif fer) is Continuny 3 bx - 2, x…

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Q: Assuming - 10x³ – 8y? - 2xy = 0 defines y as a differentiable function of x, use the theorem Fx to…

A: We need to find dy/dx at the point (-1,-1)

Q: h 2, k -1 and r 5 %3D (x - h)2 + (y- k)2 = r2 %3D %3D wwww x2 + y2 +Dx +Ey + F 0

A: Given:- h=2, k=-1 and r = 5 To find:- Equations of circle in form (x-h)2+(y-k)2 = r2  x2 +y2…

Q: '4 I x1/2 dxi n = 8 (a) Approximate its value by using the Trapezoidal Rule.

A: Given: ∫04x dx where n=8 To find: The approximation using the following, a) Trapezoidal rule, b)…

Q: Using variable separable find the GS of dy 4x + ху? %3D dx y – x²y

A: Given that      dy/dx = (4x+xy2)/(y-x2y)  We have to find the general solution by using the variable…

Q: Find the linear approximation to the equation f(x, y) = 2 ln(x* – y) at the point (4,255,0), and use…

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Q: What is the annihilator for y=x e*cos 2x ? (D²+5)2 ® D² +5 © (D²-2D+5)2 D D2-2D+5

A: See the solution.

Q: I. The Derivatives: Perform long method. 1. v = Ja2 – y? 2. x = 3t2 - 2 Vt

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Q: xp dt of dy A particular solution X, where XeC1 -2t dt Select the correct answer.

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Q: tf(x) = e2sinx. Use the local linear approximation of f at x = 0 to approximate e 2sin (0.01)

A: linear approximation

Q: dw the functions w= -5x²-3y².x= cost, and y=sint, express as a function of t, both by using the…

A: Use chain rule for derivative

Q: x+1 Evaluate f dx using the substitution u = 3x - 2 %3D V3x-2

A: The detailed solution is as follows below:

Q: y? x² 4 Find dV , where E is the solid y2 x2 + 4 z2 - <1. 9 + +

A: First we have Choose suitable parameters.

Q: 2 x' +y' x(y² –1) b. Find the points in R where f (x, y) = is continuous.

A: b. Consider the given function fx,y=x2+y2xy2-1. The above function is observed to be rational…

Q: esz+1 dz, where C:|z- 5|= 1, counterclockwise, is z - 25 The value of

A: We have to evaluate the integral ∮ e3z+1z2-25dz over the circle z-5=1. We have to find the points…

Q: 1. z dz along a straight line parallel to the x axis. (1 + i

A: Given: ∫11+i z dz To find: Value of the limit.

Q: Given f(x, y) = x³e#Y. a. Find the linearization, L(x, y), of the function at (1,0). b. Use the…

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Q: Find the linear approximation to the equation f(r, y) = 4 ln(z – y) at the point (2,15,0), and use…

A: Given: fx,y=4lnx4-y We have to find the linear approximation in two variables.

Q: dz of the function xsin(y+ z) – xy + z² = 2y. 2. Find the əx Consider, y is a constant.

A: Given equation is : xsiny+z-xy+z2=2y To find the value of ∂z∂x

Q: Find the linear approximation to the equation f(x, y) xy at the point (6,2,6), and use it to 3 = 3…

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Q: xy'=y find a general solution using separation of variables.

A: Given , The equation is xy'=y  In separation of variables we have to separate the variables and…

Q: 3t/2 Find the length, s, of the parameterized curve, x =3 e ° - 4t, y = 8 e 3t over the interval…

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Q: H.W: 1. find the derivative of the function f(x, y, z)= xy + yz + zx ,at the point P(1,-1,2) in the…

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Q: Z-f(x,y)= 2x- 2xy ty 2. 2x<y54, 0く×<23 Find absolute max and min

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: Determine the r values for which the f unction y(x) is solution of the x² + 1 equation y – 2xy? = 0

A: We have to find

Q: y? = = CX Find the orthogonal trajectories of x2 +

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Q: f(x) = is discontinuous at the point %3D 1+x² Select one:

A: We will the point where the function f(x) is discontinuous.

Q: dz of the function xsin(y + z) - ху + z* %3D 2y. Find the Consider, y is a constant.

A: Just consider y as a constant and differentiate with respect to x.

Q: the

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Q: y2 f(x, y)dx dy Let f(x, y) = e-x2-y² and

A: answer is in next step

Q: Determines a e R so that F- dr = -2 – 4 Where F(x,y) = ay, 2 e C is the part of the circumference…

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Q: 1. y = u=x? + 1 2. y= www v 3. y3D u? + 2u -3; u = Vx

A: We have to find derivative y by using chain rule.

Q: Find a point zo where the function f (2) = (z – 8 – 10i) (z– 8 – 10i)differentiable. What is the…

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Q: Cor the function f(r,y) = 3x² + 6xy + 4y², find and classify all critical points.

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Q: f(x,y) = x [(In x)2 + y2] %3D find the extreme points of the function

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Q: V4 – a2 - x2 valuate f, S Sva-a - ° ( + 2²) kz dz dy dæ – a2 – 3y? (y + z2) kz dz dy dx

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Q: xy Find the linear approximation to the equation f(x, y) = 2, at the point (2,6,4), and use it to 3…

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Q: What is the annihilator for y=x e*cos 2x ? A D2+5 B D2-2D+5 © (D²-2D+5)2 (D² +5)2

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