Write the given (total) area as an integral. * The area above the x-axis and below y = 4 - x^2 * The area between y= sinx and the x-axis for 0 ≤ ? ≤ π

Q: 1. The volume V of a right circular cone of radius r and height h is given by V = r²h. (a) Find a…

A: The derivative of f at x=a is            f'(a) = limh→0 f(a+h)-f(a)hthe instantanrous rate of change…

Q: Compute the 10th derivative of ¹ (²7²) f(x) = arctan

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Q: Let F(x) = f(x³) and G(x) = (f(x))³. You also know that a² = 14, f(a) = 3, ƒ'(a) = 10, ƒ'(a³) = 9…

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Q: Find the integral of the following equation integrate (cos x)/(1 - cos^2 x) dx

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Q: Solve the following differential equations of y" + 6y' + 5y = 10 sin (2x)

A: The given differential equation is  y''+6y'+5y=10sin(2x).

Q: Determine whether the following Consistent or not a) 5x +2y = 1 3x +2y = 1 b) X₁ + X₂-2X3 + X4 = 9…

A: Here, to check whether the given system is consistent or not.

Q: Graph the solution set. 9) y ≤ -2x + 5 3 y2x-2 -1086 ++ 2+ -10+

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Q: Solve: (1+x2)dy+ydx=0; y(1)=1, implicit solution Also: a) Determine the value of y if x=e (euler…

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Q: Find the area of the shaded region below. УА x=y² - 4y (-3, 3) Area = = x = 2y-y² FI

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Q: Consider the equation of the surface S given by -3x - 2y³z4+ xy = -4 where a and Bare pair numbers,…

A: Use formula of equation of Tangent plane

Q: Evaluating a Definite Integral In Exercises 37-42, use the Fundamental Theorem of Calculus to…

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Q: Consider the following function. f(x)=3- |x-41 (a) Find the critical numbers of f. (Enter your…

A: 1) The given function is: f(x)=3-|x-4|       =3-(x-4); if x≥43-(-(x-4)); if x<4       =7-x; if…

Q: (D² – D − 2)y - COS X

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Q: 1 find the total differential dz. z=xsin y + x² z = (2x² + 3y)² z=5x-7y

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Q: d [r₁(t) · r2(t)] = [r₁(t) × r₂(t)] : = d

A: Given: r1t=costi+sintj+8tkr2t=7i+tk

Q: Does the function satisfy the hypotheses of the Mean value there on f(x)=2x²-3x+1, [0, 2] O Yes, it…

A: We have to find the value of c.

Q: Direction: Find the integral of the following functions: 1. (5 cos x + 7 sin x) dx 2. f(3tan² x +…

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Q: 4. sinx 1-sin² x dx

A: integration

Q: Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

A: Given problem:- Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to…

Q: I want all the laws of trigonometric functions and the laws of their integration

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Q: Example 8 Video Example If it is known that + f²³f(x) dx dx = 12 and Solution By the property of…

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Q: Determine the average cost function C(x)= C(x)=x²+2x²-3x+40 Determine the average cost function.…

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Q: 63. Maximum Area A rancher has 400 feet of fencing with which to enclose two adjacent rectangular…

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Q: . Compute f(x) dx ƒ(x) = { 2x if x < 1 4 if x ≥ 1

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Q: 1. Let Evaluate the following limit. 7 (t) = (t² + 5, t²-5t+6 t²-9 lim r(t). t-3 > sin(πt)).

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Q: Find the nth Maclaurin polynomial for the function. f(x) = e-X, n = 5 P5(x) =

A: We have to find the McLaurin Series for the given function.

Q: ||r' (t) × r"(t)|| ||r' (t)||³ Use the formula k(t) = r(t) = e³ti + e-tj k(t) 12 (9 e¹ t + e−¹ t) ·…

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Q: (b) r(π/4)= (c) r(0 - π) =

A: We have to find the value

Q: If f f(x) f(x) dx = 37 and [²9(x) d g(x) dx = 12, find a Read It Watch It Need Help? √ [2²F(x)…

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Q: Find the length and width of a rectangle that has the given area and a minimum perimeter. Area: 34…

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Q: 2 1 -2 -4 X -1- -2- Write the factored form of the equation of the most appropriate polynomial. f(x)…

A: Since it is touching at x=-1 It means that there are two roots at x=-1 And one root at x=0

Q: c) The equation of a curve is y = √5x+4 i. Calculate the gradient of the curve at the point where x…

A: Gradient: The gradient is a synonym for "slope." The steeper the line is at the place the higher is…

Q: HOW ALL WORK pand the logarithmic expression using the properties of logarithms: In xy

A: Topic :- algebra

Q: Let G₁ be z = 6-√√36 - x² - y² and G2 be the upper nape of x² + y² - 3z² = 0. If S is the circle…

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Q: Match each of the Maclaurin series with the function it represents.

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Q: Find the absolute extrema if they exist, as well as all values of x where they occur, for the…

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Q: Find the derivative for each function. ㄷ 7. y=x² +2 9. y=2x²-x+3 A. 6. y=3x²-6 8. y=x²-3x+2 10.…

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Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

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Q: Find two positive numbers satisfying the given requirements. The product is 1200 and the sum of the…

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Q: Find a function f such that f '(x) = 5x3 and the line 40x + y = 0 is tangent to the graph of f. f(x)…

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Q: p(x), χ b on [a, b], which of the following is/are In f(x) continuous always true?

A: Given that q(x) is  continuous on [ a , b ]  which means f(x) is continuous on [ a , b ] .       as…

Q: Find the maximum area of an isosceles triangle inscribed inside the ellipse x²y² 1, + = a² 62 with…

A: Given problem:- Find the maximum area of an isosceles triangle inscribed inside the ellipse x2/a2…

Q: Va. a. Approximate √0.5 with the fourth order Taylor polynomial for f (x) centered at 1. b. Using…

A: To solve the following problem

Q: y" + 6y' + 5y = 10sin (2x) A..! Inne(7)

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Q: Solve for the unknown sides of the given triangle. B b 3 Additional Materials C = 30°

A: Apply the trigonometric ratio

Q: F (y)= 2 y-3

A: The given function is  F(y)=2/(y-3).

Q: Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series…

A: Taylor series : A Taylor series is the expansion of a function's series around a point. A…

Q: Evaluate Evaluate I 3 = f₁²³ x² dx 1=[rde I= dx =

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Q: Evaluate the following indefinite anti-differentiation   ∫ 5xdx

A: ∫5xdx=5∫xdx=5×x22+C=5x22+C

Q: f(x) (a) Evaluate lim X-B (b) Evaluate lim f(x) X-8 (c) Write down the equation (s) of asymptotes…

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