Let f(x, y) = 2x2y + 3xy. Use the (limit) definition of partials derivatives to show that fx(x, y) = 4xy + 3y and fy(x, y) = 2x2 + 3x.

Q: (a) Set up, but do not evaluate, a double integral for the area of the surface S with parametric…

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Q: Let f(2) = - 8 cos x + 9 tan e f (2) = (-) = C 4

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Q: Evaluate the integral (Trigonometric Substitution) x*dx J (x² + 4)² 2

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Q: 9* 3 19. P. 8" 4 P. 10 7 20. 8* 6

A: 19. P39P4820. 19.

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A: let side of triangle = x    Given

Q: f(x) f'lx) %3D

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Q: Find the equation of the tangent line to the curve y = 4sec z – 8 cos z at the point 4). The…

A: We can sole this as follows:

Q: Find the missing values assuming continuously compounded interest. (Round your answers to two…

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

Q: А. f(x) 3D Vx + 1; а %— 6 if x > 1 if x < 1 a = 2 С. f(*) — 13х + 1l; а %—-+ a = (3х — 2 В. f (*) —…

A: Only Function given in (C) is continuous at that point but not differentiable at that point. For…

Q: SOLVE THE EQUATION. SHOW YOUR COMPLETE ANDCLEAN SOLUTION. (x – 2y + 5) dx - [2 (x – 2y) + 9] dy = 0…

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Q: C is the semicircular curve drawn in the ground (the xy-plane) joining the points (0, - 2), (2, 0),…

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Q: Find the valve of k so that (2y sın x cos x -y + 2 y e** ) dx - (x - sın' x + kxye*) dy 0 becomes…

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Q: Evaluate the integral (Trigonometric Substitution) 1 (b²y6 – y®)Zdy

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Q: Use Green's Theorem to evaluate F. dr. (Check the orientation of the curve before applying the…

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Q: f (x) = X+10 x²+3

A: The given function,       fx=x+10x2+3

Q: Ha Determine Find the limit it Hie' sequence converges it the sequence Ean} converges or diverges an…

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Q: x + 7 dx J (x²)(x + 2)

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Q: Find the general indefinite integral. (Use C for the constant of integration.) | (x2 + 2x - 3) dx…

A: The objective of the question is evaluate the indefinite and definite integral.

Q: A ball is thrown vertically upward from a point 112 ft above the ground with an initial velocity of…

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Q: Evaluate the integral (2x + 6)dx x² – 2x + 17

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Q: 19. (5x2 — у) dx + xdy %3D 0

A: Given (5x2 -y)dx + xdy = 0 (5x2 -y) + xdydx = 0 Calculate whether the differential equation is exact…

Q: Assume the acceleration of the object is att)--9.8 meters per second. (Neçlect air resistance.) With…

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Q: A spring has a natural length of 30 cm. If a 27 N force is required to keep it stretched to a length…

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Q: 2x + 1 (a) lim 9x2+ x

A: We have to solve the limit

Q: 3. Compute f (x)dx f(x) = { 2x if x <1 4 if x 21

A: Given: fx=2x if x&lt;14  if x≥1 And I=∫04fxdx The Power rule: ∫xndx=xn+1n+1+C

Q: 2 (1 – :-) d.x

A: Solve the following

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A: Solved below.

Q: 143+2x+1 dx

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Q: Complete the table. (Use C for the constant of integration.) Original Integral Rewrite Integrate…

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Q: x*dx J (x² + 4)² .2

A: Trigonometric substitution in indefinite Integration

Q: An equation of the tangent line to a curve at the point (2, 4) is y = x + 2. if at any point (x, y)…

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Q: Find all values x=a where the function is discontinuous. For each value of x, give the limit of the…

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Q: Find the indefinite integral and check the result by differentiation. (e5+ sec e) de

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Q: Find the maximum and minimum values of the function g(0) = 30 – 8 sin(0) on the interval [0, T]…

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Q: (n° -9n? +16n-8)÷ (n-7)

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Q: A particle moves in the xy plane so that at any time –2 <t< 2, x = 3 sin t and y =t – 4 cost + 1.…

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Q: -IVEN DIFFERENTIAL EQUA quation 1) dx + (x -u) du = 0

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Q: 3. Anabelle would like to invite 9 friends to go on a trip but has room for only 5 of them. In how…

A: We can solve this as follows:

Q: 5. Determine the values of x for which the function is continuous. 3r +1 e. f(x)= /x – 3 2- 8 4x d.…

A: The function √(x-a) is continuous iff x&gt;=a The function 1/(x-a) is continuous iff x≠a

Q: Evaluate the integral -2x + 4 dx J (x² + 1)(x – 1)

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Q: Sketch the region enclosed by the graphs of the given functions. Determine whether it is more…

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Q: The total profit P(x) (in thousands of dollars) from a sale of x thousand units of a new product is…

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Q: Suppose an object moves along a line at 19 m/s for 0sts2 s and at 25 m/s for 2<ts5 s. Sketch the…

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Q: Estimate the volume of the solid that lies below the surface z = xy and above the following…

A: Let's find.

Q: (a) Consider A B + X-1 7x2 - 17x + 38 C (x + 6)(x – 1)²- x+6 (x – 1)² (i) Use partial fractions to…

A: (7x2-17x+38)/[(x+6)(x-1) 2]=A/(x+6) +B/(x-1) +C/(x-1) 2

Q: f(x) = {x² + 4, x > 1 (4х + 1, х < 1 at a = 1; (1,2) ||

A: From the given, to determine whicch of the following statements is False.fx=x2+4, x≥14x+1, x&lt;1 at…