I. Using the trapezoidal rule complete the following. a. Estimate the integral with n = 4 steps. (31³+t)dt = (Simplify your answer.) 0 b. Evaluate the integral directly. (3t³ +t)dt = (Simplify your answer.)

Q: Evaluate_lim_ (√9x² − 5€ +1+3″).

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Q: lim f(x) and f(x) and lim f(x) x-(-1) x-(-1)* 2 " 09 -10 of(x) 2

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Q: Find the partial fraction decomposition of 12x³ - 37x² +48x - 36 (x - 2)² (x²+4)

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Q: 3. Consider f(x) defined as follows: f(x) = 5x² + 13x + 6 |x + 2| [4 - 3x] + x, " x<-2 x ≥ −2…

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Q: -8-521-7-2 ²1₁-7-2 3-25 95-16 + 8+65 45249

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Q: Q5. Find the directional derivative of the function [f(x, y, z) = xy + y.z+z.x] at the point…

A: Please see the below picture for detailed solution.

Q: The interval(s) on which f is decreasing is/are (Type your answer in interval notation. Use a comma…

A: To find the intervals on which f is increasing:

Q: dentify and sketch the domain of f(x, y) = √x-y In (1 + y - x²)

A: solution is given below

Q: (D³ – D² – 6D)y = 12x − 2 + 5e³x – 18 sin(3x) - -

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Q: Find the derivative of each of the following A) f(x) = 128x B) g(x)=x¹8x g'(x) = C) h(x) = log…

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Q: if x - 2 Calculate the following limits. Enter "DNE" if the limit does not exist, or "oo" or "-oo"…

A: Here, the given function is: f(x)=-4x+2 if x&lt;-24x+8 if x&gt;-2

Q: 6. Sketch and label the graph of a function that describes the given situation. Pick variables for…

A: a. In this case, the population size of warthogs cannot go above 512 warthogs, so, the given…

Q: 3- 2 01 -8-7-1 T 2 -3- # Determine which one of the following rules for continuity is first violated…

A: from graph f(-1)=-2

Q: Evaluate lim X→-2 x²-x-6 x-2

A: We can find the limit of the function.

Q: 5. Use derivative rules to find the derivative of h(x) = 3f(x) - 2g(x) - x² f(x) + Show steps for…

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Q: 5. Write the given number in the polar form 2+2i a) -√√3+i b) (1 + i)18

A: A detailed solution is given below.

Q: cide whether the limit exists. If it exists, find its value. lim f(x) and (-1)¯ 6 2 T 09 lim f(x)…

A: We will find the required.

Q: Evaluate lim x-2+ 2x + [2x] x² + x - 2 2x + [2x] 2 x² + x - 2 and lim x

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Q: Calculate all four second-order partial derivatives of f(x, y) = 2x²y + 7xy³. fax (x, y) = fry (x,…

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Q: 2. Use the different differentiation rules and formulas to determine the derivative of the following…

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Q: Find the equation of the plane that passes through the points (1, 0, -1), (0, 2, 3), and (0, 0, 5)…

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Q: 3. f(x) = tan(sin x²) 4. y = log2 (5x³− x² + 1)

A: Given functions are  a. fx=tansinx2b. y=log35x3-x2+1 We have to differentiate both of them.

Q: Find the derivative, but do not simplify your answer. y = (x² + x + 2)(√x - 2√x+3) y' = Need Help?…

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Q: B: Evaluate the following: r (4)r (²) 1

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Q: The graph below is of a function f '(x) for some function f(x) with domain (-∞0, 00). 11

A: The given graph representing function f'(x) for some function f(x) with domain -∞,∞ f(0)=8 To find…

Q: 10- x - x² if x ≤ 1 2x - 3 if x > 1 Calculate the following limits. Enter "DNE" if the limit does…

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Q: 8. Find z₁ if z = xyev, x = rcos (t), y = rsin(t), when r = 2 and t = 516

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Q: The graph of f' is shown. Let f be a differentiable function such that f TT/2 TT/3 TT/6 0 -TT/6…

A: Tangent to a curve y=f(x)  at a point (a,b) is given by y-b=f'(a)(x-a)

Q: Use the graph to determine the x-values at which f is discontinuous. For each x-value, determine…

A: We have to find continuity  and discontinuity for the mentioned point. Topic :- Limit and…

Q: Suppose a is a positive real number. Determine the area of the triangle enclosed by the lines y=0,…

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Q: The graph below is the function f(x) -5-4-3-2 Find lim * 2- Find lim * 2+ 3 Find f(2) -2 -3 -5+ =…

A: Topic = Limits

Q: The interval [0,0] is closed. O True O False

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Q: 3. Let k(x, y) = ex cos(x+2y). For any (x, y) € dom k, evaluate 2k(x, y) + 4ky (x, y) — kxy(x, y) +…

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Q: хр (DZUIS-(x87 sex =h П ћp pul

A: We can find the required answer in the below steps.

Q: Solve dy/dx = x² + 2xy + y² + 2x + 2y, y(0) = 0.

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Q: 3. f(x) = tan(sin x²)

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Q: Urgent!!!

A: Given :-U=set of all real numbersp(x): x≥0q(x): x2≥0r(x): x2-3x-4=0s(x): x2-3&gt;0

Q: The table shows the position of a motorcyclist after accelerating from rest. t (seconds) (ii) (1)…

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Q: For the function f whose graph is given, state the following. (If the limit is infinite, enter 'co'…

A: This question can be solved by using the concept of graphical interpretation of limits

Q: A = -3 -30 25 1. -105

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Q: The graph below is the function f(x) -5-4 2 03 Find lim 24-1- Find lim z→-1+ da 14 Find lim 24-1 23…

A: According to the graph

Q: Given the symmetric formula:   (x + 8)/2 = (y − 6)/3 = z − 7   Find the parametric formula of the…

A: The parametric formula can be obtained by equating the equation of given line with t

Q: If g(x) = sin(x) then g'(x) = = g'(5) =

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Q: Question 12 of 12 View Policies Current Attempt in Progress Find dy dx dy dx Enter the exact answer.…

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Q: Evaluate lim x-2+ 2x + [2x] x² + x - 2 2x + [2x] 2 x² + x - 2 and lim x

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Q: 94. S 1/2dt sint 1+t² 38 WO (Hint: sin(-t) = -sin(t))

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Q: By differentation rules, evaluate the derivative of this and simplify as possible.

A: Given, y=x2+42x

Q: Q4. B. Find the tangential vector (T), normal vector (N) and binomial vector (B) for the position…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Graph the parabola and find its vertex and the axis of the parabola.   ​f(x)=​(x−2​)2       Question…

A: Topic: parabola

Q: A truck starts off 180 miles directly east from the city of Hartville. It travels due south at a…

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