Evaluate: ₁³₂₁(4x²y — z³) dz dy dx -2

Q: b. Two passenger airplanes left the same terminal at the same time. One plane flew due north at an…

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Q: The following will make the limit of a certain rational function of a as z approaches negative…

A: As we know tha rational function is of the form  P(x)/Q(x)

Q: Given the following graph of f(x) , use your understanding of derivatives to sketch a graph of f'(x)

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Q: Sy² sin Sy dy 1 A) ----² cos Sv + y sin y sin Sy + 1 256 32- 1 1 B) ² cos By-y sin Sy-256 9-11-² sin…

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Q: √2+x-√2-x X lim- --0

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Q: 312-3x| dx

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Q: 2. S 2x 2 5+2x+x -dx

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Q: 3. -3 √₁|2 - 2³ | dr da 0

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Q: 3. S. 3*sech³ (3³) 1+tanh (3*) -dx

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Q: . Reason Jupiter's gravity changes a spacecraft's path to a hyperbola as it approaches. The focus of…

A: We need to find hyperbola equation.

Q: ㅠ [sin(y) sin sin (y) sin² (y) 1+ cos(y) dy KIN

A: We will use substitution method to integrate.

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

A: We need to find derivative of given function.

Q: II. Evaluate the following integrals. 4. J 9x - 5 dx 18x + 13 9x² 6

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Q: Find the total area between the graph of the function f(x) = x + 1, graphed below, and the x-axis…

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Q: 3x(xy - 2)dx + (x³ + 2y)dy = 0; f(1)=2 Find the positive root of y at x=2. Use 2 decimal places.

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Q: [x xf (x²) dx Which integral is equivalent to the one shown: Oa) f f(u) du √uf (u) O b) S 2 O c) […

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Q: Determine the maximum value of the function f(x)=2sinxcosx on the interval [0, π]

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Q: 5. Evaluate : p.v x² -∞0 (x²+3)² 8 dx

A: Concept: Some important integration formulas: ∫1a2+x2=1atan-1xa+C Where C is constant Reduction…

Q: What is the equation of the tangent line to the curve y = at point (0,0)? O none of the choices O y…

A: Tangent line

Q: Daniel saved $260 at the end of every month for 4 years in his bank account that earned 5.60%…

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Q: Evaluate: ƒ³, ƒ²₁ √√₁²[z³(x + y)³] dz dy dx -3

A: Given :∫-33∫-12∫01z3x+y3dzdydx

Q: 7. Sara wants to show that (ā × b) × ĉ ‡ ả × (ỉ × ĉ). Yasmina says that it is impossible and comes…

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Q: The 7th derivative of f(x) = 3x5 - 12x¹ + 7x³ − 11x² + √5 with respect to a is O 360T O none of the…

A: Topic = Derivative

Q: Given F(x) below, find F'(x). Provide your answer below: F'(x) = F(x)= 2 cos (x) (1²-2) dt

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Q: The function f(x), which is defined for a ≤ x ≤ b, has the following behavior: f'(x) 0. Choose the…

A: Follow the procedure given below.

Q: Suppose y=f(x) is a curve that always lies above the x-axis and never has a horizontal tangent,…

A: Given problem:- Suppose y = f(x) is a curve that always lies above the x-axis and never has a…

Q: Determine the total solution of the differential equation (D²+8D+16)y = 64cos4x. OA.y = C₁e(-4x) +…

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Q: What is the slope of the tangent line to the curve y = T I 7 O-2 02 0 - 17/12 01/1/01 O none of the…

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Q: handwritten. Please skip

A: We assume inf B is the greatest lower bounded of B which means that it is lower bound : inf B ≤x…

Q: Use a Double-or Half-Angle Formula to solve the equation in the interval [0, 2r). (Enter your…

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Q: 4. x-1 x² + 5x+8 Ja da

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Q: 4 nd the area of the region bounded by 2x = y²+1 nd the y-axis using the horizontal strip.

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Q: A particle is moving along a horizontal line such that its velocity in m/s is given by v(t) = 2t²…

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Q: Set-up the iterated double integral in polar coordinates that gives the volume id enclosed by the…

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Q: A craftsman wants to draw a leaf repetitively on some vases. He wants to know the area covered by…

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Q: If y₁(x)=e³x and y₂(x)=xe³* are solutions to y" - 6y' +9y = 0, what is the general solution?

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Q: Question 8 Determinethe equation of the tangent line to the curve, y = 3x4-2x-1 4-x² , at x=1.

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Q: Find the are a of the region bounded by the given 1) sketch the area, ii) Determine the boundaries a…

A: This question can be solved using the concept of area under curves.

Q: 63. Use series to evaluate : Limit 1ND -cost 2

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Q: Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

A: Given that      Region R : 0≤x≤1 , 0≤y≤1-x2 , 0≤z≤4-x2+y2    Now, we take…

Q: Find the average value of f(x) = -3√x + 5x over the interval [0, 3]. Submit an exact answer using…

A: This question can be solved using the concept of average value of function over an interval.

Q: Use the definition of continuity and the properties of limits to show that the function g is…

A: This question can be solved using the concept of continuity of a function at a given point.

Q: 5x -3 2 Evaluate: f fx fdz dy dx 3x 2

A: As per our guideline we are allowed to answer only one question. Kindly repost the other question as…

Q: (1 + y²)dx + (x²y + y + 2xy)dy = 0 Ox+2y² (1+x)² = c O 2x+y2(1+y)2= O 2x+y?(1+x)2=c y² x)² Ox+y²…

A: Solving by seperation of variables

Q: 5. Find the volume of the solid generated by revolving the region bounded by y = e-x², the x-axis,…

A: Solution given below

Q: VII. Given a region R enclosed by the curves y = 1 + sin (F), 4 as shown below. (2,4) (2, 2) (-2,0)…

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Q: Find the point on the line y = 7x closest to the point (1, 0). (Use symbolic notation and fractions…

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Q: Q3. Evaluate : IL (2) * dy dx

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Q: lim (sech 2x) csch x² +0x f(x) = csch x

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Q: Evaluate the limit: lim_ (x - ln x)* x→0+

A: Using L Hospitals rule , Value of given limit is evaluated.