e²x-2x-1 x² f(x) = a) lim f(x) x⇒0+

Q: 3 − 4 + 16 - 64 + ...

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Q: Let R be the region inside the polar graph labeled "Inside" and outside the polar graph labeled…

A: We will find the region R covered from inside by r=8 and outside with curve r=-8+8sinθ.

Q: 27777 Memo No. Date 1 Mo Tu We Th Fr Sa Su Solve the following 1)√(x² + 2x²) dx if (cosx - sinx) dx

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Q: 1. F(s) = 4s+2 s²+6s+34

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Q: f(x)=xe*, a =0

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Use the binomial theorem to expand the expression (u - 5v)¹

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Q: 5. Find the general equation of the circle of curvature of the parametric equation X= ;y=+√6(t+1);…

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Q: What is the period of the graph below? sto 8+ 7+ 6+ him

A: As we can see graph  Function repeat his value after every 4 point .

Q: -3√3 dx √3 x² √√x²+9 2

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Q: Find the integral offsec²x dx tan x

A: This is a problem related to integration. based on the general formula and concepts we will answer…

Q: Find the general equation of the circle of curvature of the parametric equation t+1 X ; y = ±…

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Q: 5. Find the general equation of the circle of curvature of the parametric equation t+1 X=- 2 ; y =…

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Q: 3√3 dx √3 x² √√x²+9

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Q: Using the fact that the centroid of a triangle lies at the intersection of the triangle's medians,…

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Q: Find the length of the curve y = ln sin x from t = −2 to t = 0.

A: f(x)=y=ln(sinx) Arc length =∫ab1+(f'(x))2dx f'(x)=dln(sinx)dx=1sinxdsinxdx=cosxsinx=cotx a=-2 b=0

Q: What is the expansion of the binomial expression (x + y)⁵ ? What are the binomial coefficients?

A: Solution of given question is written in below steps.

Q: Find the critical points and sketch the graph

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Q: Give the tightest possible bound (as a Big-O of N) for each of the following functions: 1) f(N) =…

A: Given

Q: Evaluate f x5 dx - √√x6-1

A: Topic:- indefinite integration

Q: The sum of the lengths of the two diagonals of a parallelogram is 18 m. One diagonal is 2 meters…

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Q: 1- Use the shell method to find the volume of the solids generated by revolving the shaded region…

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Q: Evaluate the integral: fe²* coshada Select one: a. ++C Ob. +C O c. 2¹+C -+0 Ⓒd.+²+C

A: Simplify it .. ∫ex(e2x/2 + 1/2)dx  ∫e3x/2 + ex/2dx e3x/6 + ex/2 + c  Option A is right.

Q: Siven a = (1, 2, 1) and b - (k. 1, 2) and a × b = √35. X Determine the value(s) of k.

A: Follow the procedure given below.

Q: If the radius of a cone increases at a rate of 36 inches per second and the height decreases 2 feet…

A: Given

Q: Find the area of the region bounded by the curve y=x^3-3x^2+3 and the x-axis.

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Q: M8 1 Σ n=1 h n’ + 8 +8 3

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Q: Evaluate x³ dx (x4-5)4

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Q: Solve the system of differential equations. = - X1 6x1 + 2x2 X2' - 2x1 - 10x2 2, x₂(0) - 22 = x1 (0)…

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Q: Convert each pair of polar coordinates to rectangular coordinates 1. (2,315 degrees) 2. (1,…

A: 1) We know that relation between cartesian co-ordinate and polar co-ordinates, x=rcos(θ),…

Q: Let g be a function such that g'(x) = x (x - 3). Complete the following arguments to get all…

A: Given, g'(x) = x(x-3) We have to find the extrema from the second derivative test.

Q: An open-top rectangular box is being constructed to hold a volume of 400 in ³. The base of the box…

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Q: s dx 3x²+2x+5

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Q: c) 1/2 1 1-x² dx

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Q: Find the critical points and sketch the graph of the function.

A: Topic:- application of derivatives

Q: Water is leaking out of an inverted conical tank at a rate of 10300 cubic centimeters per min at the…

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Q: dr Evaluate - x(x²-4) ² Select one: Ⓒa.- +aresec)+c √√√²4 b. (+aresec)+c (+arcsec)+c O.C. - O d.…

A: This is a problem related to integral calculation. Based on the general formula and concepts we will…

Q: 6. Evaluate the expression sin cos (77)) 11 tan sin (sin-¹ (²-3)) 13,

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Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = 2 e* cos (yz),…

A: We can solve this as follows:

Q: 6) (-2√2,2√2) 3 3√3 8) 2 10) (-2,-2√3)

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Q: Assuming that the equation below defines y as a differentiable function of x, find the value of dy /…

A: Question- Assuming that the equation below defines y as a differentiable function of x, find the…

Q: If zs² + yt²= 1 and 2²s+y³t = ry - 4, find 0x/0s, az/at, Əy/08, Əy/ot, at (x, y, s. t) = (1, -3,2,…

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Q: clnx Find the integral of ²x ye²dzdxdy

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Q: d e) (In|sin x)) dx

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Q: Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a…

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Q: Find the gradient of the function g(x,y) = xy² at the point (3, -1). Then sketch the gradient…

A: Given:        Function gx,y=xy2   The gradient of function                  ∇gx,y=gx,gy   Taking…

Q: Find the derivative of the function y = (4x + 1)4(5x + 1)-5. dy (16x+4) 3 (4x+1)4 dx (5x+1)5…

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Q: 6 cos3x cos4x dx

A: To evaluate: ∫π6π2 cos⁡3xcos⁡4xdx Let I = ∫π6π2 cos⁡3xcos⁡4xdx We know that 2cosAcosB =…

Q: 1. Evaluate the given integral Q. = [] [²³² Q L L (x - y) dx dy

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Q: x= e-t cos 2t y= e-2t sin 2t given parametric equation find a, b, and c a) find dy/dt b) the…

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Q: Exercise (1-3): By Charpit method solve the following PDE (1): p²x+q²y=z

A: This is a problem related to partial differential method. Based on the general formula and concept…