r(t) = (3tt³, 3t², 3t+t³)

Q: x-1, if x ≤-2 f(x)=2x-1, if -2 4

A: Use bigger dots for equality

Q: 1 y = f(x) EV 5 4 3 لیا 2- 1 y 0 1 2 lim z 6 lim z 3+ f(x) = f(x) = 3 Enter each answer as a whole…

A: Need to find out the following limits.

Q: Find the area of the shaded region. 249 09 HAH प्द A B 32 3 128 3 64 3 32 6 8 10 y=√√2x y=x-4 X

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Q: lim ln x x-0

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Q: 4. (y-2) dx-(x-y-1) dy = 0, y (0) = 3

A: 4) The given differential equation is; (y-2)dx-(x-y-1)dy=0, y(0)=3. Repost the next question.

Q: Find the limit as n approaches infinity of: an = (2n²+ n-1)/n³

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Q: Find the indefinite integral. (Use C for the constant of integration.) [si sin³ 20 √ cos 20 de [( 3…

A: Let's solve given integration.

Q: 2. Consider M(x, y) + N(x, y) = 0. (a) Suppose we can find a function F example of such an equation…

A: Given that Mx,y+Nx,ydydx=0

Q: #1 #2 Cπ/2 (8 + 4 cos x) dx 0 3 [²³ - (1 − e¯x) dx

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Q: f(x) is graphed below. Find each value. 10+ 9 8 7- 10-9-8-7-6-5-4 f(x) = lim 2115 lim f(x) = lim…

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Q: Find the limit. lim X-1 lim X-1 √√x²+3-2 X-1 √²+3-2 x-1 = (Type an integer or a simplified…

A: Solution: Let the given limit is

Q: Consider the differential equation dy/dx = 5-y. (a) Either by inspection or by the concept that y =…

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Q: 28. (xy² + x − 2y + 3) dx + x²y dy = 2(x + y) dy; when x = 1, y = 1. - ANS. (xy - 2)² + (x + 3)² =…

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Q: The graphs of y = 5, y = g(z) (solid) and y=h(z) (dashed) are shown; the graph is not drawn to…

A: Solution is here

Q: If f(x) = (sin(x) S 4 + t dt and g(y) = = [ f(x). f(x) dx, find g^(1). 6

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Q: 6) Given x²-4y²-16z² = 4 (a) Rewrite into standard form and name/identify the type of surface. (b)…

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Q: 4. Use two different methods to solve the following problems. (If it's possible) a. fx(x² + 1)² dx…

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Q: A closed box is in the shape of a rectangular solid with dimensions x, y, and z. Suppose each…

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Q: 45-46 Find az/ax and az/ay. = = f(x) + g(y) 45. (a) z (b) Z = f(x + y)

A: We have to slove above questions

Q: Select the following equations that are true. 01² +2² +3² +4² +...+100² = 5050² 1 1 0 1 1 + 101 1 0…

A: Given 1.  12+22+32+42+⋯+1002=50502 2.  111011101+123456-4-5-6=234467-3-5-5 3.…

Q: To create an object to display at the Art Museum of Boston, Colleen creates a solid of revolution by…

A:

Q: Given f() following: a) g = = 6 and f'() b) h()-[ = - 6. Also let g(x) = f(x) sin(x) and h(x) - f(x)…

A: Given :gx=fxsinxhx=fxcosx

Q: lim ln x x-0

A: Given:      limx→0 ln x Left hand limit:    limx→0-ln x As can be seen, left neighborhood of the…

Q: 3 3x-1 f(x) = 4x²³²³-x + ³x-

A:

Q: Determine whether the infinite series convergent find the sum. n=1 is convergent or divergent. If it…

A: The given infinite series is ∑n=1∞34n-45n We have to find its convergent and sum of the series

Q: What is the slope of the graph? a) undefined b) positive c) negative d) 0

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Q: Evaluate the integral. x+7 2 x² +64 dx

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Q: A manufacturer produces bolts of a fabric with a fixed width. A quantity qq of this fabric (measured…

A: I am attaching image so that you understand each and every step.

Q: Find the derivative of the function g(x) = sinx - xcosx, and show work.

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Q: Find the indefinite integral. (Use C for the constant of integration.) [ sin³ sin³ 30 √ cos 30 de

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Q: [₂ (1-x-4x³. -2 •3 0 0 (1 − x − 4x³ + 2x5³) dx (5 + 3 cos x) dx 3 x² ex dx

A: Given that  some integration and we solve these integrations by using general property of…

Q: State the Green theorem in the plane. Express part (a) in vector notation.

A: Topic:- calculus

Q: C. Find the right Riemann sum for the region bounded by the graph of f(x) = √x + 2 and the x-axis…

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Q: 9 sin³ (3x) dx Evaluate O-3 cos (3x)+cos³ (3x) + C O 3 cos (3x) - cos³ (3x) + C O 3 cos (3x)+cos³…

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Q: Sketch the graph of an example of a function f that satisfies all the given conditions. lim-of(x) =…

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Q: QUESTION 4 Evaluate Stan²3x de 01 3" 01 tan3x -x +C 01 tan³3x + C tan³3x+C O tan3x - x +C

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Q: Given the function f(x) = 5x - 4, find the inverse function f-¹(x) =

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Q: lim x-2 2x² +1 3x - 2

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Q: The graph below is the function f(x) 3 2 OF -5-4-3-2-1 Find lim 24-1 Find lim 24-1¹ Olim f(x) 2411…

A: As x tends to Right side f(x) tends to -1 , therefore limx→-1-f(x)=-1

Q: If h(x) = f(x)g(x), we know h' = f'g+fg. Take another derivative and show that h" = f"g+2f'g' + fg".…

A: Here is the solution

Q: Write the first trigonometric function in terms of the second for ? in the given quadrant. sec(?),…

A: Topic : Trigonometry

Q: Find g'(3) given that f(3) = -2 and f'(3) = 4. a. g(x) = 3x² – 5ƒ(x) 2x + 1 b. g(x) f(x) . . e

A: Solution is done in steps

Q: function of x and y sın (x²₂ + y²)+2x³=yz²+2, If z is a differentiable satisfying the equation find…

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Q: (x⁹ + x4)dx (x5 - 5)1⁰ s

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Q: lim sec(x) + 7 (x, y) → (0, π/4) 4x - tan(y) sin (1) + 7 4 tan (4) X

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Q: Evaluate the indefinite integral S -10x² √1 1-x dx

A: To evaluate the integral

Q: Find a) any critical values and b) any relative extrema 3 g(x) = − x³ + 12x − 21 -

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Q: Find derivative of the function (5t^2 / 3t^2 +2)^3 using the chain rule.

A: The function is given by y = 5t23t2+23 To determine: The expression of the first derivative of the…

Q: Use the fact that sin ? =???−?−??/ 2?( e raised to the power i t minus e raised to the power…

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Q: b. 14-x²|dx

A: I am attaching image so that you understand each and every step.