1. n² Determine whether the series Σn=13n+1 ln(n+1) is convergent or divergent.

Q: Given w = y² arctan(xyz) + 2x ln(xz). Determine dw მყა dro = y² + 2 arctan(xyz) + 2x ln(xz) dy du…

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Q: If the graph of f has a horizontal tangent line at x = c and f" (c) is negative, which of the…

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Q: 26 Functions f(a) and g(x) and their first and second derivatives evaluated at z = 1 are listed as…

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Q: Sketch an angle 0 in standard position such that 0 has the least possible positive measure and the…

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Q: The following table shows the rate of water flow (in L/min) through a dam. t (min) 15 9 13 17 21 25…

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Q: Considering a continuous function f(x) = 2e³-¹ – 2x, which is true about the relative extrema of f?…

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Q: Q.1- Evaluate the following integrals (answer two only) a- So √x e-√x dx 1

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Q: √x²-3-1 x - 2 A. lim x-2 tet B. lim to et +1 C. lim x→1 x² + x - 2 x² - 1

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Q: 4. √ (3x² + 4x − 5). 8(r³+2x²–5x+5) dx

A: We have to find solutions

Q: c ( # ) **(#) tan (²) sec (²) sec ye 22 (=) sec² x² c¹² ( ² ) ye = dy O None of the choices af dy…

A: To find out the partial derivative.

Q: Sx² 1 if if > 2 x f(x) = 5 3 if x < 2 af is differentiable at x = = 2 bf is continuous at x = 2 cf…

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Q: Find all the local maxima, local minima, and saddle points of the function f(x,y) = x² + xy + y² +…

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Q: Question 2 (a) Find the derivative of the function. x3 F(x) = sin(u²) du (b) Find the area of the…

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Q: 2x³ is an antiderivative of what function? y = 6x² y = -6x² X y = -2 y = X 2

A: Integrating the given function gives the antiderivative.

Q: X-2 lim = 2 a. By L'Hopital's Rule, x→² X²-1 1 1 lim = x→2 2x 4

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Q: 7. Find the volume of the solid generated by revolving about the x-axis the region in the first…

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Q: 32 Which one of the following is the general antiderivative G(a), for g(x) Note: CER Select one…

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Q: Evaluate the following integrals. (a) (b) Sx√4 x√4 + x² dx

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Q: What is the derivative of x² + y² = 9 using mplicit differentiation? dx = xy dy dx = -xy dy dx dy dx…

A: Given query is to find the derivative of the expression.

Q: Calculus I

A: Differentiate and put the respective values.

Q: Solve the following. 1. Find the volume generated by revolving the first-quadrant area bounded by…

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Q: Which of the following corresponds to the x-4 √x-2 evaluated? 0 4 2 DNE limx→4 ( when

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Q: Problem 1. A rectangular enclosure is to be built next to a river. There will be no fence on the…

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Q: Find the area between the y-axis and the graph X = 543-2-1 1 2 3 4 5 (y - 3) dy = 6.500 (y - 3) dy =…

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Q: On which of the following intervals is the function f(x) = x3 differentiable? (0, +∞0) 0 (-00, +∞0)…

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Q: Which function is Chain Rule most useful for? Composite function Polynomial function Logarithmic…

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Q: 6. Find the volume of the solid generated by revolving about the y-axis the region bounded by the…

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Q: 5. a) How many ways can 6 people be lined up to get on a bus? b) If a certain 3 persons insist on…

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Q: Question 1 Consider the function below. f(x) = ex/x (a) Find the intervals on which f is increasing…

A: Explained below

Q: y²-6x²y=-9x ; y' at (1,3)

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Q: Given: f(x, y) = ln[1 + x siny] Find: 8² f(x,y) 8x² 2 sin y (1+xsin y)² ○ _ __ sin² y (1+zsin y)²…

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Q: Classify each differential equation as separable, exact, linear, homogeneous, or Bernoulli. Some…

A: See Explanation

Q: 1. Solve the equation 6³x+1 = 22x-3 Leave your answer in exact form.

A: We have to find out x

Q: Find the area of the region bounded above by y = x + 2 and below by y => X 542 1 1 2 3 4 5 -2 -3 O O…

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Q: A large tank is partially filled with 100 gallons of fluid in which 30 pounds of salt is dissolved.…

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Q: Given the graph below, what can you say about the function at (-1,1)? Not Continuous Continuous

A: Here we have to find whether the given graph is continuous or not.

Q: Evaluate the surface integral [[ F.ds where F(x, y, z) = (x³ +y³) i+(y³+z³) j+(z³+x³) k S and S is…

A: We will calculate surface integral , use of divergence theorem

Q: What is the derivative of y = sin (x³ sin (x³ – 3x)?

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Q: Evaluate: lim-0 (cos 2x) 2²

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Q: Given the differential equation y'' − 3y' – 4y = - 2 sin(2t), y(0) = 0, y'(0) = - = - 1 Apply the…

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Q: (8) IF: A=1+j+ k, B = i +2j- 3k Find A-B, A.B 2A.3B, A B, (A+B) (A-B) .

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Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the…

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Q: 2. Find the Taylor series expansion of f(x) = ln(3-2x) about a = 1. 2

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Q: Whatis the derivative of y = sin (2x − 1)? dx = 2 cos (2x - 1) dy dx = cos 2x dy -2 cos (2x - 1) cos…

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Q: 10 Let u= (1, 2, -1) and v= (3,-1,2) be two vectors in Rª. Which of the following is a normal vector…

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Q: Evaluate the given limit. Show your complete solution. limo(-x ln(sin(4x² - x)))

A: Let's find limit of given function.

Q: Evaluate: lime 1-sin 0+cos 0 sin 20-cos 0

A: The objective is to evaluate the limit.

Q: Solve the given differential equation by using an appropriate substitution. The DE is homogeneous.…

A: The given equation is homogeneous differential equation  (x-y)dx +x dy =0.            On…

Q: 7. Find the volume of the solid generated by revolving about the y axis the area between the first…

A: Concept: According to the shell method, the volume by revolution about the y axis is…

Q: Question 3 Sketch the following function fully: €²-2²-1 y= ²-4 Upload Choose a File

A: Given function, y= (ex-x2-1)/(x2-4)