What is the integral of 1. (1) da 2. fe* da 3. [(5x¹ - 32²) dz dx

Q: Show that the function f(x) = x + 5x + 1 has exactly one zero in the interval [-1, 0]. Which theorem…

A: Given functiin is f(x) =x4+5x+1.Now to check there is any zero in the interval [-1, 0] we use…

Q: Let sin(32) T f(x)=A, 5-√25- " x>0 x=0 x < 0. (a) Find _lim_ f(x) and lim f(x). (b) For what values…

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Q: Let f(x) = 4x²-x² c) find f"(x), the intervals on which F(X) is concave upward, the intervals on…

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Q: X The function f is defined by f(x) = +2 What points (x,y) on the graph of f have the property that…

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Q: Let f be the function given by f(x) = 300x - x³. On which of the following intervals is the function…

A: f(x) = 300x - x3

Q: Find parametric equations for the line whose vector equation is given. (a) (x, y) = (6,-3) + t(1,…

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Q: The result of a dot product is another vector. O True False

A: We have,Statement: The result of a dot product is another vector.

Q: Question 6. Use the limit definition of the definite integral to compute [₁20 + Hint: Ax = ba = *; =…

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Q: What is the slope of the curve y = 2 cos x at x = -1 1 -2 2

A: The given function is,

Q: 31. If f(x)=x+for all x = -1, then f'(4) =

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Q: Find the exact value of cos15° using a suitable half angle formula. O √1+√3 2 O√1-√3 2 1° O√2+√3 2 O…

A: Here, you can use  instead of using .

Q: Find the intervals on which f is increasing and decreasing. f(x) = -x² +2 Inx

A: the given function   for increasing or decreasing we have to find the first order derivative By the…

Q: by completing the following: (a) Partition the interval [a, b] into n subintervals of equal width Az…

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Q: Use the Law of Cosines to find the specified missing value. Approximate your answer to the nearest…

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Q: Find the point (s) on the graph of y= 4-x2 closest to the point (0,2). smetch is required.

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Q: exact value of cos²() using a suitable power-reducing formula. + √2 4 1-√2 2 1+√2 2 2-√2 4

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Q: Estimate f(2.06, 3.91) assuming that f(2,4)= 5, fx(2, 4) = 0.3, (Use decimal notation. Give your…

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Q: Find the exact value of the expression. cos(170°) cos(20°) + sin(170°) sin(20°) Need Help? Submit…

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Q: Use Stokes' theorem to evaluate F. dr. F(x, y, z) = zexi + (z - 9y³)j + (x - 5z³)k, C is the circle…

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Q: 0 18. (sin x- — π 4 π 4 1)dx + f (cos x + 1)dx 0

A: we have given integration

Q: Consider F and C below. F(x, y, z) = yzex² i + eײj + xye×z k, C: r(t) = (t² + 5)i + (t². (a) Find a…

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Q: For q (x) = -5x+5x-4 x² +2 (a) Identify the horizontal asymptotes (if any). (b) If the graph of the…

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Q: Use a software program or a graphing utility with matrix capabilities to find the eigenvalues of the…

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Q: Question 2. (a) If f is a function that is then there exists some number c such that a < c < b and…

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Q: The population of Mathvill is modelled by P (t) = (0.37) + 3, where the population is measured in…

A: The population of Mathvill is modeled by , where the population is measured in ten thousands and  is…

Q: 10. A stone is thrown vertically upward from the ground with an initial velocity of 128 ft/s. Find:…

A: Given:Initial velocity (v0​) = 128 ft/sAcceleration due to gravity (g) = -32 ft/s² (negative because…

Q: 2 Solve the following DE: (y +4x)y' = 2y = x

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Q: The graph of s = f(t) represents the position of an object moving along a line at time t≥ 0. a.…

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Q: FOR WHAT VALUES. OF A INFLECTION OF THE CURVE AND B IS (2, -16) A POINT OF GUEN BY 3 f(x) = Ax² -…

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Q: Find the unit normal vector N to r(t) = (t, cos(t)) at t = = (Use symbolic notation and fractions…

A: To find the unit normal vector  to  at .

Q: Simplify the expression. (c^(3) *a^((2)/(3)))^(-(1)/(5)) Write your answer without hsing negative…

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Q: Use the suitable product-to-sum formula to rewrite the following expression: cos (sin(*) O[sin(¹) -…

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Q: Find an equation of the plane. the plane through the point (8, -2, -6) and parallel to the plane z =…

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Q: Use Lagrange multipliers to find the absolute maximum and minimum values of the function f(x,y) =…

A: We have to find the maximum and minimum values of given function.We will use Lagrange's Multiplier…

Q: 0) Findu'ify=" (elan(t), 1) dt

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Q: d) y = In(arc cos x)

A: y = ln ( arc cos x )

Q: The following triangle depicts the case of the Law of Sines (AAS). 40⁰ B O True 22.5° O False

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Q: Consider the following vector field. F(x, y, z) = 3xye²i+yzexk (a) Find the curl of the vector…

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Q: Let f be the function defined by f(x) = 1/ X What is the average value of f on the interval [4,6]?

A: The given function is:

Q: points) Consider the function f(x) = (a) Write f(x) as a piecewise function. Evaluate lim x→-6+ f(x)…

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Q: 32. f(cotx - tan x)² dx

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Q: Find the angle between the vectors v = 5i - 3j and w = 2i - j. Round your answer to the nearest…

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Q: Use derivatives to determine where f(x) = 2x^3 - 9x^2 + 12x - 3 (a) where the function is increasing…

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Q: Find an equation of the plane. the plane through the point (6, −3, 6) and perpendicular to the…

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Q: 2 3 -1-3p² +p² +³p_dp -2 P

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Q: Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle. a = 10, b…

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Q: Find the equation of the tangent line to the curve y=x^2 when x=pi. Please provide the answer in…

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Q: Find an equation in cylindrical coordinates for the rectangular equation Entry Tip #1: To enter ,…

A: We have to find cylindrical equation of the the rectangular equation

Q: Convert the point (x, y, z) = (-3, 3, 5) to spherical coordinates. Give answers as positive values,…

A: To convert the point  to Spherical coordinates.

Q: F Ifv = i +2j and w = 3i + 6j, then the projection of v onto w is: O i+2j O-31-6j O 11-2j 3i+ 6j Q…

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