25. lim √√1 + 2x - √√1 - 4x X x-0018 101

Q: Question 1 Let 0 = cos¯¹(-³) where 0 ≤ ≤. Find the exact value of 0.

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Q: 3. Find the equation of the line or plane a) Plane parallel to the lines r= (1,2, -3) + t (-1,0, 4)…

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Q: Let cos a with 0 < a < Find the exact value of tan(a + B). and sin 8 = - with <3 <³

A: Let  with  and  with .To find the exact value of .

Q: Evaluate the integral. (Use C for the constant of integration.) 5 dx 49x² - 1 √x².

A: The given integral is:

Q: dw 3 Evaluate at t= for the function dt 2" xy w(x,y,z)= x= sint, y=cost, z=t². Z O A. O B. O C. O D.…

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Q: Given the function h(x)= x(x-4)', find the following characteristics of its graph. Critical point(s)

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Q: ∞ Determine whether the series Σ e n=0 N13 converges or diverges. If it converges, find its sum.

A: We need to find sum of the series.

Q: The base of a three-dimensional figure is bound by the circle x² + y² = 4. Vertical cross sections…

A: We need to find area of rectangle.

Q: Find the derivative of the function at the given point in the direction of A f(x,y,z) = 7x - 10y-3z,…

A: The given function is; f(x,y,z)=7x-10y-3z, (6,5,4)A=3i-6j-2k

Q: Find the limit, if it exists. (If an answer does not exist, enter DN x² + y² 0 lim (x, y) → (0, 0) X…

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Q: If you know that Q(x) is a quadratic function and that Q(3) = 12, Q(10) = 11 and Q(1) = 10 then: - |…

A: If you know that  is a quadratic function and that and , then to evaluate the following integral.

Q: Given f(x)= (a) lim f(x) 4-6- (2-3x x 6 (b) find each of the following: lim f(x) x-6+ (c) lim f(x)…

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Q: Solve the equation: sin(2x) - cos(2x) = 1 over the interval [0, 2π).

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Q: Show that f is continuous at a if and only if f is continuous* at a.

A: Using, alternative definition of continuity we can show easily that f is continuous function

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A: To determine the magnitude of the resultant force and the angle it makes with the smaller force, we…

Q: Integrate the function f over the given region. f(x,y) == over the square 5 ≤x≤7, 5 sys7 xy

A: The given function is:

Q: For what values of x does the series converge conditionally? (-1)+1(x+4)n ngn Σ n=1 O A. x= -13 O B.…

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Q: Use the graph below to find the indicated limits. If a limit doesn't exist, state DNE. If value…

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Q: Use the convolution theorem to find the inverse Laplace transforms of: (a) F'(s) = (8² +9) ² (b)…

A: Given

Q: Find the limit. lim (x,y) → - (49-49) 2 2 x+y#49 x+y-49 √x+y-7

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Q: 15-28 Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and…

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Q: Decompose the following fraction using a long division: 5x³ + 2x² - 38x - 21 x² - 9 a = b = 5 0 C =…

A: The given term is; (5x3+2x2-38x-21) /(x2-9).

Q: π Find T, N, and k for the plane curve r(t) = -5ti- 5 In (cos t) j, −2 <t< T(t)=)i+)j RIN 2

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Q: We will evaluate the following improper integral: ∞ I 1.₁0. dx (x2+3)2 First we will do the…

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Q: dw Evaluate at (u,v)=(5,1) for the function w(x,y) = xy-y²; x = u-v, y= uv. ди OA. -1 OB. 9 OC. 4 O…

A: Put

Q: A region bounded by fly) = y, f(y) = 6 - y, and x = 1 is shown below. Find the volume of the solid…

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Q: y = 7 cos(x), y = 7 - 7 cos(x), 0≤x≤ π

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Q: Find the maximum and minimum values of the function f(x, y) = x²y subject to 5x² + 4y² = 60 =

A: The function isf(x,y) = x2 y5x2+ 4 y2 = 60Let g(x,y) = 5 x2+ 4 y2 -60Differentiate f(x, y) with…

Q: Express the area of the region bounded by the given lines as an iterated double integral. The…

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Q: Integrate the function f over the given region. 1 f(x,y)= over the square 8≤x≤9, 8≤y≤9 xy

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Q: The formula x(x) = |f''(x)| 3/2 expresses the curvature of a twice-differentiable plane curve as a…

A: The function is

Q: I find the domain and the range for the for the following function a) f(x,y) = 3x-y² by f(x,y) =…

A: Given that :a) f(x,y)= 3x-y2b) f(x,y)= √2 - x + yWe find domain and range of this function.

Q: Use Simpson's Rule and all the data in the following table to estimate the value of the integral S y…

A: The data of x vs y is given as x3456789y-8-5-11469

Q: 4. a) b) Let x = 2ī + 3j - k, y = i- j + 4k and 2 = −3ỉ + j. Express the vector x + 2y - 37 in terms…

A: Let , and (a) To express the vector  in terms of vectors  and .(b) To determine .Note: Since the…

Q: (b) Describe the relationship between each set of planes, and solve the system if possible: (i)…

A: Here we have given the system of planes consists of three equations:Now, comparing the coefficients…

Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y)=5e-5ye* Select…

A: Given function:-

Q: Find aflax and aflay. f(x,y) = 2x²y af əx af ду || ||

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Q: Find the indefinite integral. (Use C for the constant of integration.) 1 1 x2 20x + 105 - dx

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Q: 1 -1 √1-y² 0 X [Q² + y 0 (x² + y²) dz dx dy

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Q: Write an iterated integral for a. vertical cross-sections, b. horizontal cross-sections. OA. S S dy…

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Q: Eric spent a total of $50.75 at the school bookstore. He bought a calculator for $29.75 and some…

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Q: In Exercises 17-28, use the Direct Comparison Test to determine whether the infinite series is…

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Q: Write an iterated integral for a. vertical cross-sections, b. horizontal cross-sections. SS dA dA…

A: We need to write limits of integration.

Q: Integrate the function f over the given region. 1 f(x,y) = over the square 4 ≤x≤6, 4≤ y ≤6 ху

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Q: A chemical manufacturing plant can produce z units of chemical Z given p units of chemical P and r…

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Q: 8. Three forces of 5N, 8N, and 10N are at equilibrium. Determine the angle between the two largest…

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Q: Consider the following cost function. a. Find the average cost and marginal cost functions. b.…

A: C(x) = 0.04x^3 +0.02x^2 +30x +90, 0&lt; x &lt; 1500, a = 1000The marginal cost function is the first…

Q: Write a rule for the linear function. y -4 -2 45 5 5 -1 -19 -22

A: A table of values is shown below :

Q: 1) Find: lim x→ 4 x² - 16

A: We are required to find:

Q: The position of Minnie the mouse, as she moves back and forth along a horizontal line is given by…

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