s dx √x-1 +√x+1

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A: This is question of calculus  here one function is given  we solve using application of…

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A: Finding the definition of derivative.

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Q: 1. Consider the following, recursively defined function C(1) = 1 C (2) = 1 - C(n) = C(C(n − 1) + C(n…

A: We need to prove that C(n)=1 for all n.

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Q: प. #5 X Ay rotate X=AX X70 about x-axis (Find veterane)

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Q: Leave all answers in exact form (not rounded) Evaluate the improper integral or state that it is…

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A: Given query is to graph the equation.

Q: if x^2 + y^2 + z^2 = 9,  dx/dt = 5, dy/dt = 4, find dz/dt when (x,y,z) = (2,2,1)

A: If x2+y2+z2=9, dxdt=5, dydt=4. To find dzdt when x, y, z=2, 2, 1.

Q: A function f has the following verbal description: "Multiply by 7, add 9, and then take the third…

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Q: 5. Consider the line that connects points (3,1) and (5,5). Find the surface area of the solid…

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Q: Let f(x) = 4√x If g(x) is the graph of f(x) shifted up 4 units and left 3 units, write a formula for…

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Q: TOPIC 1 Higher Derivatives 1-x Q. #1 Given f(x)= please find derivatives below. Hint: Always…

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Q: Suppose that one factory inputs its goods from two different plants, A and different costs, 4 and 10…

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Q: Find d dx d dx 2 8x² 3 8x² 3 7 2 5x² 7 2 5x =

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Q: 13. r(t) = t sin ti + e' cos tj + sin t cos tk ht

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Q: 5. Find the linear appoximation for the funciton f(x, y) = (ro, Yo) = (3,0). x-y xy+1 at the point

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Q: Find the sum of the infinite geometric series 2+2(2x-1)+2(2x−1)² +2(2x-1)³ +... if |2x-1|<1.

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Q: 3 [(82³-18x) dx = dr Show work and explain, in your own words, how you a

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Q: Consider the differential equation x²(y + 1) dx + y²(x − 1) dy = 0 Classify this equation by: order…

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Q: Write an equation of the circle with center 4,-5 and radius 12

A: Given query is to find the equation of the circle.

Q: Find the instantaneous rate of change for the function at the given value. f(x)=x² + 4x atx=1 The…

A: Given query is to find instantaneous rate of change.

Q: Consider the following LP problem: maximize z = 5X1 + 2X2 + X3 subjected to X1 + 2X2 + 3X3 <= 30, X1…

A: Given linear programming problem as follows ,  Max Z =   5 x1 + 2 x2 +   x3 subject to…

Q: 5. Evaluate the following limits 5ху (a) lim (x,y)-(0,0) x² + y²¹ 5ху (b) lim(x,y)-(1,2) x² + y² ·

A: Solving both subparts,

Q: 2 For the functions w= -9x+8y.x= cost, and y= sint, express dw as a function of t, both by using the…

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Q: Find all values of a such that the vectors = and are perpendicular

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Q: 4 Let u = (7,-3) and v = (4,8). Find O A. О в. O C. 19 5 OD. 12 44 (+) 5 . (8.12) D 5 1+ 3 -V.

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Q: Find the indefinite integral on the domain of positive real numbers. Enter an exact answer. Remember…

A: The given integral ∫4x+65xdx. We have to find the value of integral.

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A: This is a problem related to integration. Please follow the procedure given below.

Q: Find v u if v = 3i+ 4j and u = 2i +6j. A. 6i+24j OB. 5i+10j OC. 30 OD. - 18

A: Given query is to find indicated dot product.

Q: Clear denominators in the following partial fraction decomposition and determine the constant B. 5x²…

A: Given;  (5x2+46x+73)/(x+8)(x+3)2= 1/(x+8) - B/(x+3)-4/(x+3)2

Q: Evaluate the indefinite integral [sin³t sin³t cos² tdt = + C

A: V=∫sin3tcos2tdtwe know sin2t+cos2t=1∫tndt=tn+1n+1+cd dx(cosx)=-sinx

Q: Find an equation of the tangent line to the curve at the given point. 1 + sin(x) cos(x) (π, -1)

A: y=1+sinxcosxpoint is (π,-1)equation of tangent line is y=mx+cwhere m is slope=dydx

Q: The directional derivative of z = f(x, y) at (1,5) in the direction toward the point (7, 4) is 17…

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Q: Let a₁ = 1 2 a,₂ = and b= 4 - 20 h For what value(s) of h is b in the plane spanned by a, and a₂?…

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Q: In the attached calculation, why does it say it is the quotient of the two polynomials? Does that…

A: Please see the below answer.

Q: Find the center and the radius of the sphere. x² + y² +z²-3x + 2z=0 The center of the sphere is (0…

A: The given equation of sphere is: x2+y2+z2-3x+2z=0 To find the center and the radius of the sphere.

Q: Question 3 Find y(2) given the IVP (3xy+3y-4) dx + (x + 1) ²dy=0;y (0) = 0 16 27 - 12 17 O 13 25 07…

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Q: Fin d Y = 4 = 1X₁ Y=0 - -0 2 X=0 X=1 volume + Kotate about x-axis

A: Please see the below picture for detailed solution.

Q: Find the distance from the point S(5, -6,6) to the line x = 10t, y = 6t, and z = 7t. The distance is…

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Q: Find the equation of the tangent plane to the surface determined by at x = 4, y = 2. 2= || 2 = 35 -…

A: z=35-x4y4at x=4, y=2equation of tangent plane is…

Q: Find the length of the following two-dimensional curve. /₁² =(1/2. (2t+1)3/2 3 r(t): for Ost≤8

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Q: x²+4x x²-12 2 x²+x-6 x²+x-6 (Simplify your answer. Use integers or fractions for any numbers in the…

A: To solve the fractions.