Find the equation of the tangent line to the graph of the function f (x) = sin (7√) at the point (7²,0).

Q: Find the transition points. y = 5x³ + 120x² (Use symbolic notation and fractions where needed. Give…

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Q: 1. Consider the function f(x) = x6 - x³. a. Determine the absolute extremum using the First…

A: The given function, f(x)=x6-x3

Q: f(x)-f(a) a. Use the definition mtan = lim x-a x-a b. Determine an equation of the tangent line at…

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Q: 5. x x2 + x − 6 dx

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Q: Find the limit of the following sequence that the limit does not exist- or determine. {(₁ + + )"}…

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Q: sin (8x) sin(x) dx

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Q: In the quadratic equation Ax²+BX+C =0 The roots are real and distinct. The roots are complex…

A: The given quadratic equation is Ax2+Bx+C=0

Q: Determine the x- and y-intercepts for the given function. B(x)=5x+8

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Q: Find the complete solution of ds dt = 5t* √√s.

A: Given problem:- Find the complete solution of dsdt = 5t4√s

Q: Find the Area of the Surface obtained by rotating the curve about the x-axis y = cosh x, 0≤x≤1

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Q: A bicycle with 20-inch diameter wheels is traveling at 17 mi/h. Find the angular speed of the wheels…

A: To find out angular speed and number of revolutions per minute.

Q: Find the area bounded by the parabola x = 8+2y-y², the y-axis, and the lines y = -1 and y = 3.

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Q: The population of a town is decreasing at a rate proportional to its size. In 1980, the population…

A: The population of a town is decreasing at a rate proportional to its size.In 1980, the population…

Q: Find the derivative of the following functions. Use long method. a. f(x) = 3x² + 5x - 100 b. f(x) =…

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Q: df Use integration to find f(1) when f(3) = 1000 and = 4(x+1)(x² + 2x)³. d x -24,272 -26,341 25,980…

A: Integrate on both sides of the given differential equation and find f(x) .

Q: xdy = (5y + x + 1)dx Ans: y

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Q: S St. Not e (cos48)² 45 ds

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Q: Consider the position function s(t) = -4.9t +31t+24. Complete the following table with the…

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Q: Question Find the area A of the region that is bounded between the curve f(x) = 4 sin (4) g(x) = 4…

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Q: The area bounded by the parabola ay=x², the x-axis, and the line x=b is revolved about the y-axis.…

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Q: Let x = 11t², y = 9t6 - 2t². d²y Determine as a function of t, then find the concavity to the…

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Q: crowave oven is stands for the number of units produced. 100 000 C(x) = 0.002a³-0.06x² +120x+5000,…

A: Please refer to the image below

Q: Find f. f(t) = 5e¹ - 6 sin(t) — 5 f"(t) = 5et + 6 sin t, f(0) = 0, f(π) = X 0

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Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, —12t) (a) If Ř(0) = (-1,4,-5),…

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Q: Given x - ³²+2y — In(y + 1), find the arc length for 0 ≤ y ≤4 8

A: The arc length of the curve x=f(y) for a≤y≤b is given by ∫ab1+dxdy2 dy

Q: 1. Given: parametric curve H defined by r(t) = tan-¹ t and y(t) = e¹, where t € R (a) Find the slope…

A: Solved below.

Q: 1f S₁ (x+5) dx = Sº (x+5) dx = 14, then the value of b is equal to If A) None B 3 с 4 D -3 E 2

A: We have to find the value of b.

Q: Show that the function f(x, y) = e2x cos(3y) satisfies the partial differential equation 4f + fyr =…

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Q: 2x³ - 4x² − x − 3 dx x² - 2x - 3 zln |x+1| +31n|x - 3| + C Option 1 2 In x + 1-3 ln|x - 3| + C…

A: Given, ∫2x3-4x2-x-3x2-2x-3dx

Q: Find the set of symmetric and parametric equations of the line passing through the point P(3, 4, 1)…

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Q: √√7 - t³, cos t³) t³, c 3 R(t) = (sin t³,-

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Q: Find the area of the region bounded by y=x²-1, x=2 and y=0. Use horizontal element and express area…

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Q: 1. Solve the differential equation (x-4y-3) dx-(x-6y-5) dy=0

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Q: Find the area bounded by the curves x² + y = 6, y = x, y = -2 and x = -2.

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Q: Find the transition points. f(x) = x(17x)1/3 (Use symbolic notation and fractions where needed. Give…

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Q: A rectangular field having an area of 2500m2 is to be enclosed by a fence, and two additional fence…

A: Area=L×W=2500 m2 So,L=2500W The perimeter P=2L+2W+2W {to divide the field into three 2 fences of W…

Q: 1. Evaluate the line integral of E = xax - y ay along the segment P₁ to P2 of the circular path as…

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Q: 4. Find the limit, if it exists. If the limit does not exist, explain why. 3x²+4-4 (a) lim x2x² - X…

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Q: xpand the logarithm as much as possible. Rewrite the expression as a sum, difference, or product of…

A: We  have simplify above questions

Q: a. Use the definition mtan = lim f(a+h)-f(a) h h→0 b. Determine an equation of the tangent line at…

A: As we know that; The slope of the tangent line to the curve is equal to the derivative of the…

Q: Find a particular solution of ds 1 dt =cos-t determined by s=3 when t == 2 3 wha

A: Given ,    dsdt=cos(t/2)

Q: 1. Consider the function f(x) = x6 - x³. a. Determine the absolute extremum using the First…

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Q: dx ex√4-e²x the integrand is transformed into? (a) cos² 0 (c) sin² 0 (b) sec²0 (d) csc²0 When the…

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Q: 2π 3 [³* sin(y) + sec² (y) dy

A: We have to evaluate the given integral.

Q: Using trigonometric substitution, A) None Ⓡ/ B Ⓒ D sec58d0 tan²0 tan40d0 sece * sinᎾdᎾ cosA Ss x4dx…

A: ∫x4(1+x2)32dxPerform trignometric substitutionSubstitute x=tan(θ)→θ=arctan(x)→dx=sec2θ dθ

Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: 1 (b) lim x →0 sin² x 12/200…

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Q: Integrate the following functions f(x)=Ln [sec (x)] [², 3]

A: We will see the graph of secx to judge the value of greatest integer function of secx.

Q: (b) p = 2 sin p cos 0

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Q: Solve • ƒ²₂(x + 1)(x + 2)²(x² - 1)dx with and without the even-odd theorems (show both solutions).

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Q: C. Find the volume of the solid obtained by rotating the region bounded by y = -10 + 6x-x², x = 1…

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