Given that f(x) = x² g(x) = x + 15, find 11x and | (a) ƒ + g = (b) ƒ – g= (c) fg = (d)

Q: 4) Show that the circumference of the unit circle is equal to 1 dx (an improper integral) 2 1 – x² E...

A: We need to verify the circumference of circle.

Q: Error Analysis. Below is the solution (possibly, with errors) for the derivative of the given functi...

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Q: find the maximum or minimum value of the function f(x)= 3x^2-18x-160 _______

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Q: 2-3 Let f(x) = %3D x-2 a. Find the intervals on which the function is increasing and decreasing. b. ...

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Q: Let f(x) = 2x + 2x 5 Use the limit definition of the derivative to calculate the derivative of f: f'...

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Q: ' (x5–x³– 6x) dx is the same as x²+2 A |(13- 3)dx |(+3)dx В 4x dx x²+2 D x³+x- 8x dx x²+2 E .3 x'+x-

A: Solution: ∫x5-x3-6xdxx2+2  

Q: 2. Sally is trying to choose between two internet plans. Under the first plan, AT&T will sell her a ...

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Q: Consider the function f(x) given by the graph below. y f(x)

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Q: Problem: 5 coordinates are given: A(-1, 4, 5), B(2, -1, -2), C(-6, -8, 3) in RCS; D(5, n, -12) in CC...

A: Given coordinates: In Rectangular Coordinate SystemA=-1,4,5B=2,-1,-2C=-6,-8,3In Cylindrical Coordina...

Q: Solve the separable equation using the integral factor  y⁴ y¹ + y¹ + x² + 1 = 0

A: Here, the given differential equation is: y4y'+y'+x4+1=0⇒y'(y4+1)=-(x4+1)⇒(y4+1)dydx=-(x4+1)⇒(y4+1)d...

Q: Evaluate the following integral: 23: tanh 7tx dx

A: Given that: ∫tanh(7πx)dx

Q: y = tx2 + tx dy Find dx dy dx + 2tx * dy Find dt dy dt II

A: Given that y=tx2+t4x We have to find dydx  and dydt dydx is the derivative of y with respect to x dy...

Q: Calculate the Taylor polynomials T, and T3 centered at x = a for the function f(x) = 19 1n(x + 1), a...

A: Taylor series of function fx at a is defined as:       fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+…=0+ddx...

Q: Between 2006 and 2016, the number of applications for patents, N, grew by about 4.1% per year. That ...

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Q: A matrix that is not square can still have an inverse.

A: Inverse of a matrix.

Q: eros voR-SI ioNO WDW WCLN PCMath 12 - Rev. 2019 3. Find the general solutions rounded to two decimal...

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Q: I. Find the limits of the ff by applying the limit theorems. 6. lim vx² + 5x + 2 1. lim 2021 x→12 x→...

A: 1. limx ~12 2021, function f(x) = 2021 is independent of x limit is 2021   2.  limx~7 4x - 3 putting...

Q: Based on empirical data, scientists have determined the following function that models the height of...

A: Given that: h(t)=3.2t

Q: Let R be the region bounded by y = 7 sin(z), y = 7(x – 2)*, and y = 3x + 4, and containing the point...

A: R be the region bounded by y=7sinπ2x, y=7x-22 and y=3x+4that contains the point 2,7.

Q: find the point (x,y) at which the graph of y=7x2+5x-6 has a horizontal tangent line.  The function ...

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Q: Find the cartesian equation of the following: 6 1. r = 3-sin 0 2. r2 cos(20) = 4 %3D 9. 3. 4 sin(20)...

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Q: Let f(x)= -6x^4+8x^3+72x^2 a) lim x-> +inf f(x) b) lim x-> -inf f(x)

A: Here, the given function is: f(x)=-6x4+8x3+72x2 Here, note that the leading coefficient is negative.

Q: sin() 8. n2 ilamsili n=1

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Q: #) =+2x9ー5×y +3, fnd: (a) Oz そe dy

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Q: Find the area bounded by the curve y=4sinx and the x-axis from x=1/3 to x=1. O 6 sq. units O 8 sq. u...

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Q: Find f if f"(x) = 4 – 6x, f(0) = 3, and f(2) = -2. %3D Answer: f(æ)

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Q: Given f(x)=−2x^2+4x+13, find f′(−4) using the definition of a derivative.

A: f'(a) = limh→0 f(a+h)-f(a)h.

Q: If possible, rewrite the equation in slope-intercept form, y = b+ mx, and give the values of b and o...

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Q: t y = t dy Find dx 1 8t dy dx t dy Find dt dy dt + II II

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Q: 10- 1,0 F1 10

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Q: Lan® do In (cos0) 3.

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Q: calculate the mass of the surface, knowing that the density at each point is proportional to the dis...

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Q: Suppose that V(t) = (21)1.07' + 5 sin(t) represents the value of a person's investment portfolio in ...

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Q: Solve the separable equation using the integral factor  2xy + 6x + (x²-4)y¹ = 0

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Q: QUESTION: Find the area in the first quadrant bounded by the coordinate axes and the parabolic arc V...

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Q: The equation of motion of a particle is s = 2 - 912 + 4t + 2, where s is in meters and t is in secon...

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Q: Use the Intermediate Value Theorem to show that there is a root of the equation in the given interva...

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Q: Suppose that a room containing 800 cubic feet of air is originally free of carbon monoxide. Beg t = ...

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Q: Find the following using the table below. 1 2. f(x) f'(r) 4 2. 3 4 3 2 4 3. g'(x) 4 3. 1 h'(4) if h(...

A: Topic:- function and it's Derivatives

Q: x² –1 Evaluate lim X→1 Vx+1 Hint: Direct substitution will result in the expression "O" "O". To reso...

A: Given: limx→1x2-1x+1

Q: Show how to use the Intermediate Value Theorem to show that the equation z – V4z = 7 has a solution ...

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Q: Find the equation for the plane through the points Pol- 1,5,- 3), Qo(-5,4.2), and Ro(3, -5,0). Using...

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Q: Solve for the differential equation: x (y -1) dx + (x+1) dy = 0. If y = 2 when x = 1, determine y wh...

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Q: Vx m = (b) Find equations of the tangent line at the point (1, 5). y = Find equations of the tangent...

A: Topic:- application of derivatives

Q: If the demand for q units of a product priced at $p per unit is described by the equation 200 V29 + ...

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Q: Consider the graph of the function f(x) shown below. y List any x-values at which f is not continuou...

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Q: Find the equation of the family of orthogonal trajectories of the system of parabolas y? = 2x + C. y...

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Q: (1) For every natural number n, x" = nx"-1 (you may use the product rule for derivatives and that x ...

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Q: Let F(x) = f(r°) and G(r) = (f(x))° . You also know that a = 12, f(a) = 2, ƒ'(a) = 15, f'(aº) = 5 Th...

A: We know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x   Given: Fx=fx9 ; Gx=fx9a8=12...

Q: lim COos x –1 x→0 x² – x³

A: To evaluate the given limit.limx→0 cos x-1x2-x3