Apply the first derivative test to indentify all relative extrema. f(x) = cos² (2x)

Q: 2 Find the center of the following equation.      x 2 +y 2 + 8x - 6y - 15 = 0 (4, 3) (8, -6) (-4,…

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Q: For each of the following integrations, choose the method that can be used to find its solution.…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Determine the values of r for which the differential equation y' +9y = 0 has solutions of the form y…

A: Given differential equation.

Q: IV. Do as indicated. 1. Let f(x) = where = 1. 1 Find the equation of the tangent line to the graph…

A: Let's find.

Q: 2. Specify on which intervals is f increasing/decreasing and where the graph of f is concave…

A: First derivative test: If the first derivative of the function is positive over an interval, then,…

Q: O parabolic cylinder

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Q: A 0 B) 48 32 D) 96 If f cos42t dt = At - B sin 2t cos 2t + D sin 4t cos 4t + C where A, B, C and D…

A: The given problem is solved below in detail.

Q: A continuous O Ext F(XI = Find ***** V-V- K x has CDF X Co oxx cl 15X value of k 16 17 18 19 20 21…

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Q: IV. Do as indicated. Use Squeeze Theorem to evaluate lim sin(sinh x) csch z.

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Q: e2x+Inx² sin x² dx -+fe²x cos x² dx

A: This is a problem related to integration. Based on the general formula we will solve the problem.

Q: The conic section whose equation is x2 - 3y2 - 8x + 12y + 16 = 0, is ______. centered on the origin…

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Q: Identify the center of the conic section whose equation is 4x 2 - 25y 2 - 8x - 100y - 196 = 0. (-1,…

A: We can identify the center as below.

Q: 6x5-25x+8x3+43x²-8x-12 4. Find (3x+-11x² +9x²-11x+6) (9x²+12x+16) -dx if this can be reduced to 63…

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Q: Given The boundary of C: 0 ≤ x ≤ π,0 ≤ y ≤ sinx With Green's Theorem, Evaluate this line integral. $…

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Q: 11. lim [w ln (1-2)] In 3w

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Q: Integrate the following functions f(x₁y) = (x-1) =x over the given regions y=x²

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Q: II. Find Do not simplify your answers. dr 1. log,(√2x² + y) + tan(x² − z³) = sin¯¹(x² − 1) + −

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Q: Solve the given differential equation. All solutions should be found. dy 2xy + y² + 7 dx x² + 2xy…

A: To find the solution of given differential equation in implicit form.

Q: Solve the given differential equation. All solutions should be found. dy 3x² - 7y - y³ 7x + 3xy² dx…

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Q: III. Suppose that a function f(x) satisfies the following properties, together with the table of…

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Q: 12 Give the properties for the equation 9x 2 + 16y 2 - 36x + 96y + 36 = 0 Domain -6 ≤ x ≤ 7 -7 ≤ x…

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Q: if any. Find the absolute extremum point(s) of f(x) = el-cost on [−5, π],

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Q: Solve the given differential equation. All solutions should be found. dy 3x = e +9y dx NOTE: Use c…

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Q: 1. Evaluate the following limits. Using L'Hôpital's Rule is not allowed 3. lim (x-3) tan(9-x²)…

A: We will calculate the limits by Limits rule

Q: Find the equation of the vertical asymptote and the equation of the slant asymptote of the rational…

A: Given: fx=36x2-12x+36x-3   As we know that; To calculate the vertical asymptote, equate the…

Q: 1. Evaluate the following limits. L'Hopital's rule is NOT allowed |2x - 1| tan-¹(¹) 2x - 1 . lim…

A: LetL=limx→ 0-2x-1tan-11x2x-12x-1 is negative when x→ 0-.  Therefore 2x-1=-(2x-1)L=limx→…

Q: fe²x+Inx² sin x² dx = e2x cos x² dx

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Q: Using production function Y = K1/2 1/2 and using the information below: Relative to US column 4…

A: Solution of the problem as follows

Q: Given the function C(a) = (x-4) (x + 6) (x - 1) its C-intercept is its x-intercepts are

A: Solution is given below:

Q: 62. du * |x|dx

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Q: Find fzyr. f(x, y, z) = x³y5₂6 + xy³ + yºz

A: Given: fx,y,z=x3y5z6+xy3+y6z We have to find fzyx For fzyx we first have to find the partial…

Q: orrect. a k(t) ||r' (t) × r"(t)|| ||r' (t)||³ = r(t) = e¹0ti + e-tj tc

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Q: y = 2 x + 2 -3+x

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Q: Definite Integral and Plane Areas of integration (snow solution) 3 1. dx Sö = 2 1+x 4 dx 2. Sh 25-x2…

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Q: dy II. Find Do not simplify your answers. dx 1. log; (√2x² + y) + tan(2* — 7³) = sin¯¹ (2²-1) + - Б

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Q: (measured counter- 1. A circle with radius 2 is centered at the origin (0,0). For an angle clockwise…

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Q: You have found an annuity that will pay 4.75% annually and you plan to put $1,000 into the annuity…

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Q: (A) = and B D = . Find the vector projection of A onto 2A - BO O O O none of the above

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Q: Question 7 Given : A B E 0 2π 3 F|+ π 4 (U) =|m x³sin(2x) dx = 3 5π 6 3πt 4 277²-24 64 Find bif sbst

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Q: if f(X)= SINX+2X+1 and g is the inverse function of f, what is the value of g'(1) ?

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Q: Sπ/4 ___xª dx (x²+4)5/2 (Use trigonometric substitution)

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Q: ♫♫¹⁄² sin (*) cos (*) sin (²) dx (Consider initially the first 2 terms)

A: Solving the definite integral.

Q: Find the slope of the normal line to the graph of g(x) = = at the point where x = 0. sin¯¹(x)+e²

A: Slope of the Normal line to the curve f(x) is -1f'(x).

Q: -2 + อน Ore 0

A: Suppose uxy=0 , denotes u = uy implies uy = 0 uxy = F(x) + G(y)  ,satisfies uxy = 0 a) y du/dxdy +…

Q: (C) EXERCISES Evaluate the following integrals: 1. tan² x dx 2. cot cot² r dr COS I da sin x COST…

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 3. lim x-3 (x-3) tan(9-x²)…

A: As L'Hospital's rule is not to use so I have used the expansion of sin and tan function and easily…

Q: Describe the end behavior (long run behavior) of f(x) = 28 As → →→ ∞, f(x)→ ? As I→ ∞, f(x) → ? v

A: This question can be solved using the concept of limits.

Q: Integrating Factor by Inspection: 9. (x4y+)dx + xy³dy = 0

A: Let the differential equation is of the form Mx, y dx + Nx, y dy = 0  ...........(1) If Mx+Ny≠0 and…

Q: Exatuate the integral QUS √3x xام واح

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Q: Find the partial derivatives of f(x, y) = x³y²

A: Solution ) f(x ,y ) = x3 y2 a) Partial differentiation with respect to x  fx( x ,y ) = 3x2y2 [ y is…