Find the curve whose slope at any point (x,y) is 6x^2−2x−5 if the curve is required to pass through the point (−1,−6)

Q: Let f(x) = x - 25. The arc length of the graph of f(x) over the interval [6, 10] is given by the…

A: Topic = Integration

Q: Find the sum and express the answer in its lowest term. 3 =N 4 10 1) 9 3 2) + 13 6. 4 3) + + 7. 9.…

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Q: Solve 7 cos(2w) = 7 cos (w) – 3 for all solutions 0 < w < 2n w = Give your answers accurate to at…

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Q: 3. Consider the vector field F(x, y) = (2xy, x² – sin y). Evaluate %3D F. ds where C is the curve…

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Q: Solve the following initial value problem. f′′(x)=−36x^2−18x−4,f′(−1)=13,f(−1)=−35

A: To solve the initial value problem.

Q: 1. Use deductive reasoning to show that the following procedure produces a number that is equal to…

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Q: Find the area of the region that lies outside the circle r = 3 cos and inside the cardioid r = 1+…

A: Given r=3cosθr=1+cosθ

Q: d) Find the inverse : y = (x + 2)2

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Q: What is an exponential function and a logarithmic function?

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Q: Find the sum of the first 100 terms in the arithmetic series 1+2+ 3+4 + ... + 100.

A: To find the sum of first 100 terms of given arithmetic  series.

Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. 3…

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Q: Determine the Laplace transforms of 3, 0 12

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Q: In what way did theorems/techniques of antidifferentiation help you find the integral of an…

A: Given

Q: 2r 2r If the total volume of the cylinder and square block is 30 cm', express h in terms ofr.

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Q: The series 1 + Vn? 1+ Vna 00 n=1 is convergent if and only if: Select one: 72 a > Ob. 35 a * 35 4 O…

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Q: in(2x) – 5 cos(x) = 0 for all solutions 0 < a < 2n .68

A: Please refer to the image below

Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y) = e 2x2 + y? - 8x…

A: To find out all the local maximum, local minimum and saddle points.

Q: blem #1: Differentiatef (x ) = [(4 x4 -5 )(3 x2-9 x - 5 ) ]3 and solve f (2).

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Q: Slove this equation -2/x e y dx =1 1 x / dy

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Q: Find the area of the region bounded by the graphs of y2 = 4x and the line 2x – y = 12

A: answer is in next step

Q: Consider the following integral. |Fe dt Find a substitution to rewrite the integrand as - Le" du. u…

A: To find the value of given integral.

Q: Find a point on the curve x + y = 25xy other than the origin at which the tangent line is…

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Q: Assume that the radius r of a sphere is expanding at a rate of 70 cm/min. The volume of a sphere is…

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Q: 2x³-4x-8 2. S; dx (x²-x)(x²+4)

A: Topic:- integration

Q: Question 5 The approximate value of -31.8 using linear approximation, imaginary O (E) None of the…

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Q: 1. Find the area bounded by the parabolas y? = 4 and y²+12x = 36 2. Find the Area bounded by the…

A: Given :     Curves and find area by integration

Q: Consider f(x) = cos (x) ln(x +2). a. Find the local linear approximation of f(x) at æo (In 2 =…

A: linear approximation of function fx=cosxlnx+2, at point x0=0

Q: Solve the initial value problem for r as a vector function of t. dr 9 Differential Equation: diz+…

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Q: y – 2. Suppose the symmetric equations of lines l1 and l2 are = 2 - y = z and a = -1, 2…

A: x-12=2-y=z implies L1 : x-12=y-2-1=z-01x=-1, y-23=z-12 implies  L2 : x+10=y-23=z-12If lines L1 and…

Q: Graph each parabola. Identify the vertex, focus, directrix, endpoints of the latus rectum, and the…

A: We have to sketch graph of parabola then identify the vertex, focus, directrix, endpoints of the…

Q: If x = t^2 + 1 and y = t^3, then the second derivative is? (Show your complete solution). a. 3/(4t)…

A: Given that,   x=t2+1 and y=t3

Q: Practice Problems. Find all of the first order partial derivatives for the following functions. (a)…

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Q: dx 2+

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Q: Basic Catalus 1. f(x)- f(xth) = 5 (x +h) - Sx - 3 lim 5(x+h)-3- [5x-3] = lim 56 +5h -3 - 5% +½ h-70…

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Q: x - 1 Suppose the symmetric equations of lines l1 and l2 are = 2 - y = z and a =-1, 3 y - 2…

A: Given: The equations of lines are, l1: x-12=2-y=zl2: x=-1, y-23=z-12 Concepts used: The equation of…

Q: 2. of the image graph in terms of x? y 2-3 C. y= 2(1-x+2|- 3) D. y= (1-2x+ 2|-3) A. y= -|2x +2|- 3…

A: Consider the graph

Q: In Exercises, the given vectors form a basis for a subspace W of R' or R'. Apply the Gram-Schmidt…

A: The given vectors of ℝ3 are: x1=110, x2=342

Q: Integrate f(x.y,z) = x+ Vỹ - z° over the path from (0,0,0) to (1,1,1) given by C,: r(t) = t i+t°j, 0…

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Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

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Q: Next ques Use the Integral Test to determine if the series shown below converges or diverges. Be…

A: Here, the given series is: ∑k=5∞9kln2k

Q: V9 – x² .2 .2

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Q: Use the Integral Test to determine if the series shown below converges or diverges. Be sure to check…

A: Let's find.

Q: Find the slope of the tangent to the graph of f(x)=x(1-x2) at its point of inflection.

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Q: Question 4 Each side of an equilateral triangle measures 3cm, with a possible error of 0.1cm. Using…

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Q: Using the definition of differentiation, find the value of f'(a) if f(x) = sinx

A: Topic = Derivative

Q: The difference between two angles, how is the result of the same trigonometric function

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Q: Problem #1: Differentiatef (x ) = [(4 x4 - 5 )(3 x2-9 x -5 ) ]3 and solve f (2). Solution: Reason:

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Q: Suppose f(x) = 10 (a) The rectangles in the graph on the left illustrate a left endpoint Riemann sum…

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Q: 3:) Consider the function g defined by g(x ,y) = cos (TXVG) + logg (x-y) 3 (b) calculate the…

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Q: 1. Evaluate the following integrals. csc 0)(1+ sin² 0 + sin 0 cot² 0) do a.

A: To find out the integration.