Definite Integral and Plane Areas of integration (snow solution) 3 1. dx Sö = 2 1+x 4 dx 2. Sh 25-x2 = = 10/²/2 3. 527 = dx X-X¹3 32/2 in 153

Q: Using trigonometric substitution to solve: f sin 2x +C 8 cos x√3-cos²x 1 + C 8 secx√4-sin²x sin 2x…

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Q: Question 14 If f(x)=x+4 and g(x) = -4, (a) f(g(x)) (b) g(f(x)) (c) Thus g(x) is called an function…

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Q: C. y = 5x² + 2, x=0, x=2, y = 0

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Q: Find an equation of the plane containing the point (3,0,-4) and perpendicular to the line r(t)=…

A: A detailed solution is given below

Q: II. Find d Do not simplify your answers. 1. log,(√2x² + y) + tan(z* — x") = sin−¹(x² − 1) + ½

A: This question can be solved using the concept of differentiation of implicit function.

Q: Consider using the method of partial fractions to solve dx x²+x+1 2x²+2+x³+x - dx = [Aƒ (x) − B…

A: Given problem:-

Q: Find Duf at P. NOTE: Enter the exact answer. Duf = f(x, y) = sin(3x – 4y); P(4,3); u || 35 i I

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Q: π/4 x³ dx (x²+4)5/2 ST/4 (Use trigonometric substitution)

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Q: f/² () sin cos (sin (²) dx (Consider initially the first 2 terms)

A: To evaluate: ∫0π2sinx3cos4x3sin2x3dx Let I = ∫0π2sinx3cos4x3sin2x3dx We know that  sinxcosy =…

Q: If f cos42t dt = At - B sin 2t cos 2t + D sin 4t cos 4t + C where A, B, C and D are constants, 2A-3B…

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Q: List intervals on which the following function is INCREASING. Use INF for infinity, use no spaces,…

A: The given function,    fx=3x2-1

Q: dw a) Find for the following function. dt w = 2ye* -In(z), x = ln(t2 + 1), y = cos(2t + 2), z = et…

A: If w=f(x,y,z) and x =g(t),y=h(t) , z=u(t) then,    dwdt =∂w∂x.dxdt+∂w∂y.dydt+∂w∂z.dzdt. Note : As…

Q: If f cos42t dt = At - B sin 2t cos 2t + D sin 4t cos 4t + C where A, B, C and D are constants, ...…

A: Given ∫cos42t dt=At-Bsin2tcos2t+Dsin4tcos4t+C To Find 2A-3BD

Q: y″ −3y′+2y=e¹x ; y"

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Q: List the absolute maximum and absolute minimum of f(x) = x³ 12x on the interval -3, 1]. Give the…

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Q: Find the radius of convergence, R, of the series. 8 n Σ (x-a)", b>0 bn n = 1 R= Find the interval,…

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Q: d Calculate[ri(t) · r2(t)] and 77[r1(t) × r2(t)] first by differentiating @[r₁(t) the product…

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Q: Find the total area bounded by the x-axis and the curve y = f(x) on the indicated interval. f(x) =…

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Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: We have to integrate the given function for the given limits

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: (D4 − 1)y = 0

A: D4-1y=0

Q: The radius of a circle increases at a rate of 2 m/s. Find the rate at which the area of the circle…

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Q: 25 1. ƒ x²√5 − x²dx = − ²x(5 − x²) (5 − 2x²) + ²5 Arcsin (5x) + C 2009

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Q: 1 x√x²-2x =dx : √x²-2x x =+c C

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Q: what is the normal equation to the curve which is the circle with center at origin and and radius of…

A: Given circle , With center at origin (0,0) And a point on circle is (4,3)

Q: Using trigonometric substitution, what is √x²-9dx ? f x3 A sec (-) √x²_9 6x² +C B ¹ (1) - V +C (ⒸC)…

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Q: Find polar equation for the Cartesian equation 13y = 8x. a. theta = 1.02 c. theta = 0.55 d. r = 0.55…

A: Substitute x=rcosθ and y=rsinθ in 13y=8x. 13rsinθ=8rcosθ  13sinθ  =  8cosθ

Q: Write an equation for a rational function with: Vertical asymptotes at x = 5 and x = -2 x-intercepts…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: 19. -π/2 21. -π/4 23. [³5e* dx sin 0 de cos x dx sec² 0 do (2x secx tan x) dx 20. rπ/3 22. 24. [¹-dx

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Q: Use the formula k(t) k(t) = = ||r'(t) × r"(t)|| ||r' (t)||³ = 10t: r(t) = e¹⁰ti + e-tj to find k(t).

A: This question is related to vectors, we will solve it using given information.

Q: Question 7 10 -8 -6 -4 -2 8 10 -2- -4 -6 -8 -10 Write an equation for the graph, where y depends on…

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Q: 7. Determine all relative extrema or saddle points: f(x, y) = 4x³ + 8xy - 2y²

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Q: Explain why you think the sequence converges to a finite number or (n+1)! diverges. If the sequence…

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Q: Given the function f(x) = -6 x -9 Evaluate f(8) = Find a when f(x) = 3 I

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Q: VI. Suppose h' is continuous at x = 0 and h'(x) =tan(2x) - 1 if x > 0. Find h(0), if it exists.

A: Let's find.

Q: The annual revenue and cost functions for a manufacturer of cat toys are approximately R(x) = 540x…

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Q: Given the function f(n) = 3n¹ +33n³ +90n²: its f-intercept is its n-intercepts are

A: We can find the intercepts as below in the following steps.

Q: Calculateri(t) r2(t)] and r₁(t) x r2(t)] first by differentiating dt the product directly and then…

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Q: Two copies of the same Rational Function are shown below. On the graph below draw the Horizontal…

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Q: Use r = 6cos(7 θ) and r = 6

A: r1 = 6                                              1r2 = 6cos7θ      θ ∈0,π…

Q: dp p(-75+25p²) 2 S. Trigonometric Substitution

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Q: 1. f/² sin (1) cos (4) Sir sin (²) dx (Consider initially the first 2 terms)

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Q: 1 sinx+cosx+1 -dx

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Q: dx tan x +sinx+1 Half-angle Substitution

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Q: Given: (1+2x) ex dx. Using integration by parts and letting u = − 1 − 2x, dv = f(x)dx, then the…

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Q: /² sin sin ( π/4 x² dx (x²+4)5/2 (Use trigonometric substitution) fe2x+Inx² sin x² dx = = Find f…

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Q: (3x-x²) dx x² Reciprocal Substitution

A: Let's find.

Q: The region R enclosed by the curves y=x and y=x^2 is rotated about the x-axis. Find the volume of…

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Q: Find the average rate of change of g(z) = 4x + 5 between the points (-4,-11) and (3,17)

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