]: Show that the following functions are linearly dependent f₁(x) = tanx, f₂(x) = -tanx, f(x) = 2tanx.

Q: 53. Prove the following limit formula for e: e = lim (1 + x) ¹/x x⇒0

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Q: Find the derivative of the function. y = V 11x + +√ 11x + y' = X √11x

A: Given query is to find the derivative of the function.

Q: Show that (u-v) > Show that u xv||² Find the

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Q: For both parts, sketch and shade the 2D region, draw a typical disk/washer, and set up the integral…

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Q: 9. X n=1 10/22 2n²

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Q: lim1 X→0 limx x→0 1 The function f is defined by lim lim x 0x x0x lim x→0 x² +1 X lim x→0 x²-1 f(x)=…

A: Simplify the expression of f(x) then set the limit.

Q: Letf (x)=- 2x+9 ifx1 ffisnotcontinuousatx=1, Determine whetherf (x) iscontinuousordiscontinuousatx =…

A: NOTE: Refresh your page if you can't see any equations. . . the function is not defined for x=1  so…

Q: Find the derivative of the function. y = xe8x y' =

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Q: i

A: We have to choose the correct option from the given options according to the given information

Q: Prove that the lateral surface area of a right circular cone with height h and base radius r is S =…

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Q: Determine whether the given differential equation is linear or nonlinear, and give its order. yy'''+…

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Q: 生 二三 2 1

A: The given series is sumnation of 1/(n2-1) , n from 4 to infinity.

Q: Find the area bounded between y = x² and y = -(x + 2)² + 4.

A: Topic = Area

Q: 2. Let R be the region in the first quadrant that lies below y = 1-x². Use the shell method (method…

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Q: -6-5-4-3-2 3 2 1 1 2 -3 2 OF 2 QUESTIONS REMAINING f 1 2 3 4 5 4 5 6 X Identify the points of…

A: A graph is said to be discontinuous at a point x=a iff the graph takes rwo different values at x=a(…

Q: Use the graph to determine the limit. (If an answer does not exist, enter DNE.) (a) (b) (c -8 -7 lim…

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Q: 1) y = 3z³+2 2) y = 1 t²+1 x = z² +4 x = √4t+1

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Q: 5. 0= n n!

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Q: Eliminate the arbitrary constants in the equation defined by y = ax^2 + bx. Which of the following…

A: The given equation has two arbitrary constants so it has to be differentiated twice for elimination…

Q: 2. Newton's law of cooling states that the temperature of an object changes at a rate proportional…

A: If the temperature of the object is T and the temperature of the surroundings is T' then by newtons…

Q: Sin (x+y) house buy and at - dx up no Please

A: As per our guideline we are supposed to be answer only one question you can repost other question in…

Q: dy/dx+y/x=xy^2 use y=v/x

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Q: If x = √x^5y^5 + x^2y + xy^2, find:   zy zxy

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Q: Find the area of the given region. Use a graphing utility to verify your result. 1 + In x³ X 1.418 y…

A: We will integrate y from 1 to 2 to find the required area.

Q: dy = y2-4 dx y (6) = 2

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Q: 1 ² dx 1-x

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Q: - 2 to The region bounded by the line 2x + 3y = 6 and the x and y axes is rotated around the line y…

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Q: dy Solve the differential equation cosx- -+ysinx=sinxcosx. dx A y = sinxlnl secxl+ Csinx B) There is…

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Q: 23. (In x)² dx

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Q: (i) Let F(x) be a power series. Then the radius of convergence of F(x) can be negative.

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

Q: Suppose the rational function f(x) meets the following criteria, • limc f(x) = ∞ • limc+ f (x) = -∞…

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Q: Evaluate the definite integral: [ 2√5x-2 dx =

A: Given query is to find the value of the integral.

Q: a. Construct a rational function whose only asymptotes are y = 4 and x = 1, and whose x intercept is…

A: Given that Asymptotes y=4   horozontal asymptotes.x=1  vertical asymptotesx intercept is 14,0y…

Q: (d) Let p(x) and g(x) be non-zero polynomials. Then we can use Integration by = p(x) and v' = p(x)…

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Q: Use the graph of f(x) = log 1/3x to graph the function f(x) = log 1/3(x-5). Then give the domain and…

A: NOTE: Refresh your page if you can't see any equations. . the given parent function is  now we need…

Q: Find the area of the given region. Use a graphing utility to verify your result. 1 + In x³ X y= y

A: Concept: The area of the region bounded by the two curve f(x) and g(x) such that f(x)≥g(x) on the…

Q: 1. FIND THE FIRST PARTIAL DERIVATIVES ev u+v² f(x, y, z) = ln(x + 2y + 3z) W = zexyz d) w = e) f)

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Q: Consider f(x) = 2\sqrt(x) a) Find f '(x) using the 4 step process ( f(x + h) - f(x)/h) where h is…

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Q: A- Find the volume of the solid generated by revolving region Under the curve (y=4-x²), about x = 2

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Q: Question 8 Given this graph of f'(x), sketch f(x) given that f(0) = 80. -20 -10 30 25 20 15 10 -10…

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Q: PROBLEM 1 [DOMAIN OF FUNCTIONS]: Find the domain of the function: sin 3x √x²+4 f(x)=

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Q: 8. Solve xy' (2y - 1) = y(1-x) A. In (xy) = 2 (x - y) + C B. ln (xy) = x - 2y + C C. In (xy) = 2y -x…

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Q: onsider the function g(x) = 5 - 4x + x² If the lim g(x) = 1, then what is the value of a x→a 0 1 O-2…

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Q: For the pair of functions f(x) and g(x), find f(g(x)), g(f(x)), and f(f(x)). f(x) = x¹; g(x) = 3x -…

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Q: 21. cos(sin-¹)

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Q: F5 % X 5 10:18 1…

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Q: An automobile depreciates by 20% per year. How soon will it be worth only half its original value?…

A: Solution :let, time periods = n yearsoriginal price of a car= pprice of a car after n years =…

Q: 2. Compute (16−1/16)4.

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Q: Find the time required for an object to cool from 320°F to 220°F by evaluating the following where t…

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Q: Find an equation of the line that is tangent to the graph of f and parallel to the given line. Line…

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