Find the derivative of the function. g'(t) = g(t) = (8t + 8)² (8t² – 8)−3 -

Q: y s 5 4 -2 -2 The diagram shows the shaded region bounded by the curves y = x² + 2, y = 4 - x, y = x…

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Q: Answer

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Q: The integral of 3^4x dx is equal to A^AY Ing+ 0

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Q: x-1 x² + 5x + 8 S dx

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Q: If (2, 1) is a critical point of f and fzz(2,1)ƒyy(2, 1) < [ƒzy(2, 1)]², then ƒ has a saddle point…

A: Here, the given statement is: If (2,1) is a critical point of f and fxx(2,1)fyy(2,1)&lt;fxy(2,1)2…

Q: If F(x) = = [₂√₂ x² a. F'(1) b. F(2), by interpreting F(2) as an area √4t - t² dt, evaluate the…

A: Given: F(x)=∫x20 4t−t2dt To find : F'(1) and F(2)

Q: What is the volume in cubic units of the solid formed when the region bounded by y = x^2 and y^2 = x…

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Q: What is the general solution to the differential equation (tan x)dy - (4y In y - y tan³x)sec²x dx =…

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Q: Convert the degree measure to radian measure. Round to three decimal places. −46.23°

A: Convert the degree measure to radian measure. Round to three decimal places. −46.23°   Please show…

Q: Set up the double integral that will find the volume of a solid bounded by z = 1- y²x² and the xy-…

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Q: Evaluate the limits using the L'Hopital's Rule. lim (tan x) (sin x-1) x+2+

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Q: Evaluate the following integrals. 1. S 1- coth² (log2 x) x cosh(log₂ x) -dx π 3 (sin³ x) VT…

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Q: Evaluate ²(2x + 3e* - 1) dx a. 12.43 b. 13.45 c. 14.24 d. 15.23 e. NONE OF THE ABOVE

A: Given problem:-

Q: Find the general and the particular solution: d²u du = 4(1 + 3v)²; u = -1,and = -2 when v = -1 dv²…

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Q: 1-10 J = exp(-x²)dx 0 Evaluate J by means of Simpson's rule with n = 2m = 10 and h = 0.1

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Q: Why is it =10πr33? particularly, why is the value 33?

A: Let's solve.

Q: TU Evaluate a sec²20d0 8 a. 00.33 b. 0.5 c. 0.67 d. 0.25 e. NONE OF THE ABOVE

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Q: S 36x2+25 - dx

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Q: 5. Use Cartesian coordinates to evaluate ㅋ yy dv where D is the tetrahedron in the first octant…

A: Let's evaluate given integral.

Q: Question Eight y s 8 7 5 4 14 4 3 -2 -1 The diagram shows the shaded region bounded by the curves y…

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Q: Sketch the graph of r = 0 90° +2

A: To sketch the graph of r=θ90°+2.

Q: (Requires a short but nontrivial geometric argument.). Let ABC be a triangle with angles…

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Q: 5. Simplify: y23 x7 O x7 y ¹5 15 x7 y15 O x7 y 2³ (x5)-2 x ¹ y ² 3 xy-3 (y-6) ³

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Q: 1. (2x6x5 +7x³-3x² - 11) dx 2. f(9y2 +6y-4-y-5+1) dy (12x-x+x) dx 3.

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Q: 2.) Obtain the solution of the following initial value problem! (t-2)x' - x = 2(t - 2)², x(0) = 1.

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Q: (6) Sketch a graph of a function, f, that has the following properties: • lim f(x) = 3 and lim f(x)…

A: Given information:  ----------------------------------------------------------------------------…

Q: Evaluate (2x + 3e* - 4) dx a. 12.43 b. 13.45 c. 14.24 d. 15.23 e. NONE OF THE ABOVE A О в Oc O D DE

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Q: ab c Pq r U V W a. det (2B¹) where B = 4u 2a 4v 2b -q 4w 2c <-r 2p -a+u 3u b. det (20¹) where C =…

A: Given problem:-

Q: Evaluate the following integrals 2x ·S- -dx 2 5+2x+x

A: We know that ∫duu = lnu+C ∫1v2+a2dv = 1a·tan-1va+C

Q: Find the volume of the colld_generated by. revolving the area bounded by the given curves_ about the…

A: We need to find volume.

Q: Find by integration the area of the region bounded by the curves y=x2 and y=−x2+4x. Include a quick…

A: Use area under curve

Q: Find the lateral surface of the cone generated by revolving the line y = mx from x = 0 to x = 1…

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Q: Given: cos 3y + sin 2x 2 cos 2x 2 O -3 sin 3y-3 -2 cos 22-2 O -3 sin 3y 3 O -2 cos 2x-2 3 sin 3y 3 2…

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Q: Determine the following integrals: 1.1.1 ļ (cos2x+sin x) dx x+1 .1.2 1₁ JF dx x + 2x+1 2 1.1.3 | ₁…

A: ∫ sin(ax) dx =-cos(ax)a+C       and     ∫cos(ax) dx =sin(ax)a+C ∫xn dx = xn+1n+1+C Note : As per our…

Q: Using the shell method, what will be the equation of the volume of the solid formed when the region…

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Q: The total cost of producing 1 unit of a product is given by C(x, y) = 80+ 0.3x² + 50y - xy dollars…

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Q: Perform the integration. (sinh x)(coth x +csch3x) dx +

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Q: y = coux, X = Find the are a OF i) sketch the area. ii) Determine the boundarier by ) Set-up the…

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Q: 2. lim (x - Inx)* x)² 2-0+

A: Here, the given limit is: limx→0+(x-ln x)x which is (-∞)0 form.

Q: 1. Why is it important to use the six trigonometric ratios in getting a missing angle value?

A: The six trigonometric ratios are sine, cosine, tangent, cotangent, secant, and cosecant. Basically,…

Q: Stan 3x sec 3x dx 3.

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Q: The Philippine Postal Service will accept a box for domestic shipment only if the sum of its length…

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Q: Your farm encompasses 900 acres, and you are planning to grow soybeans, corn, and wheat in the…

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Q: Find the area (in square units) bounded by the parabolas x² + 2y - 8 = 0. a. 7.10 sq. units b. 7.01…

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Q: Find the equation of the line tangent to y = e The equation of the line tangent is y= at x = 1 - In…

A: Given query is to find the equation of the tangent.

Q: 6. A family wants to build a fence in their backyard for their dogs, Charlie and Linus. The enclosed…

A: Given:     Area = 4000 sq meter

Q: 3. +∞ 8 -∞ dx x² + 1

A: Given ∫-∞∞dxx2+1To evaluate the integral:

Q: 9. A child is flying a kite with a 45-ft string at an angle of elevation of 50°. Which of the…

A: Let's find altitude of the kite in feet.

Q: u=-5), v=-1-√31 (a) Find u-v. U-V= (b) Find the angle between u and v to the nearest deg 0

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Q: F T M 3. Let et = 2 . Find a power series nào ng t² a) Find a power series for te . obtained in @)…

A: We want to evaluate the power series of the given expression and want to integrate it.