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Q: 1. sin x sin 2x + cos x cos 2x = COS X

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Q: If √x + √y = 12 and y(1) = 121, find y'(1) by implicit differentiation.

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Q: If an > 0 and an converges, then (-1)"an converges. Select one: O True O False

A: Absolute Convergence test :The absolute convergence test states that, If ∑n=0∞anconverges then,…

Q: 12 76 Exercises (if possib 15. y = 5x + 3 17. y = -x - 1 19. y − 5 = 0 0 1 23. 7x - 6y = 30 020…

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Q: - 7. Find the area bounded by the curve y² + x − 4y = 5 and the y — axis

A: We have to find the area of the given curve and line.

Q: Question 5 (i) Use the diagram below to find sin(0), cos(0) and tan(0). (ii) If sin (500) -1…

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Q: Determine the limit of the following by using l'hospital's rule

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Q: Find the the e following: sinx first maclaurin four Series nonzero for terms of each (21) S² Tara d…

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Q: -(x-a)² - 1, 7. g(x) = tan x (x + b)² + 1, x>7 What must a and b be for the given function to be…

A: Given :

Q: What is the indefinite integral (anti-derivative) { cos(x) dx? ○ sin(x) + C cos(x) + C - sin(x) + C…

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Q: 3. xy = a², y = 0, x = a, x = 2a.

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Q: Find the slope of the tangent line to the curve − 3x² – 1xy – 3y³ = at the point (-2, − 1). 11

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Q: Find all local extreme values of f(x) = - The FIRST local extreme value, moving from left to right…

A: Topic:- application of derivatives

Q: 2. Captain Crunch wants his airplane to travel along a path that is [N60°W] with a groundspeed of…

A:

Q: Find the arc length of the curve on the interval. r(t) = t²i + 12tj, 0≤t≤ 6 The figure shows the…

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Q: 150 5 -4 -2 100 50 -50 -100 -150 200! 2 4 6 8 Xx

A: We know that, The highest point the graph ever reaches is the absolute maximum. The lowest point the…

Q: 2x e²x cos(y)dx + e* sin(y)dy = 0

A: This question is related to differential equations, we will solve it using given information.

Q: from X-TT to x=3TT/2

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Q: Find -(4²). Type In(x) for the natural logarithm function. da (4²)

A: Topic = Derivative

Q: Find the arc-length function s(t) for the line segment given by r(t) = (9 - 9t, 40t). s(t) = Write r…

A: Given :- r(t) = <9-9t, 40t> for arc length

Q: -6-5-4-3-2-1 у 6 5 4 3 2 1 -1 -2- -3 -4 -5 -6 7 123 456 X

A: To find the range of the given graph.

Q: -) 5cos(x +40°) - 3.6 = 0

A:

Q: Is the following piecewise function continuous? if x < 0 0<if x < 3 if 3 < x f(x) = -3x² x - 3, . -x…

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Q: What is the derivative of k(y)=(6y^−1+3y^−2)(6y^−3+4y^−4)?

A: The given function is: k(y)=(6y-1+3y-2)(6y-3+4y-4) We have to find it's derivative with respect to…

Q: - п/2 эт/2 п/2 0 п/2 3г/2 5г/2

A:

Q: 1. A rectangle has a perimeter of 14 m. Express the area of the rectangle as a function of the…

A:

Q: -6-5-4-3-2-1 у 7г 6 4 3 2 1- -1 -2 -3 -4 -5 -6F 1 2 3 4 5 6

A: Range :- all the y value where function is defined

Q: 225 ft ☐☐ X A building that is 225 feet tall casts a shadow of various lengths as the day goes by.…

A: Topic- Application of derivatives

Q: 2. Find the domain and the critical points of the following func- tions on their domain: g(x) = 3x5…

A: Concept: Domain: Domain of the function is the set of all the inputs over which the the function has…

Q: Calculate the following definite integral: 2x² + 5x dx

A: Given ∫022x2+5xdx

Q: Find F as a function of x and evaluate it at x = 0, x = 7/4, and x = 7/2. 1-² sin € F(x) = F(0) =…

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Q: 12. Find the area bounded by the curve y = 3x(x - 2)² and the x axis.

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Q: Let the position function of a particle be r = (t, t², 0). Find the normal component of the…

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Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

A: Given in the figure A1 = 7 , A2 = 3,  A3 = 2  and A4 = 2. Concept:-  If In [a,b] y = f(x) ≥ 0 then…

Q: 2 94

A: according to question function is f(x)=x+4 x=1,2,3,4 f(1)=1+4=5 f(2)=2+4=6 f(3)=3+4=7

Q: Basic Level 1. The graph shows the total cost of making compact discs. 250 Namibian Dollars…

A: According to the graph :-cost of 0 compact disc=N$50 thousandscost of 5 thousands compact disc=N$80…

Q: Find the length of one turn of the helix given by r(t) == cos(t)i + sin(t)j + 1 1 99 25 -tk.

A:

Q: 5. Determine whether the following are rational numbers: (a) 2² +27¹; (b) log₂ 3; (c) 2+√2. (d) If…

A: We have to find if the given numbers are rational or not.

Q: U V U a) f(x) = sin x The trigonometric function pictured here is b) f(x) = csc x O c) f(x) = sec x…

A: we need to find which trigonometry function has the following graph

Q: Find the shortest distance r1 between the two lines given by r₁ (t) = (3 + t, 3t, 5 – 4t) and r₂ (t)…

A:

Q: The surfaces p= 3 and 5, p = 100° and 130°, and z = 3 and 4.5 identify a closed surface. (a) Find…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Calculate (t) when k(t) = r(t) = (6t¯¹, 1, 6t)

A: r(t)=6t-1, 1, 6t Formula for  curvature κ(t)=r'(t)×r''(t)r'(t)3

Q: - -5 -4 -3 -2 1 - 1 y 5 3- N 1- 1 -2H -3- 1 2 3 4 5 X

A:

Q: 10. Given two vectors u = [6,2] and v=[-2,1], determine the projection of u on v.

A: #10

Q: f(x) = √x²-2 7+|x6| S if x < 2 if x ≥ 2

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Q: 2. 3. (32²+7)dx=(2,₁¹²₁ )dy = 0 4) 1 xe²x dx + (5-1)dy = 0, y(0) = 0 1

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Q: (b) If f(x)= |x-1| is now restricted to the domain x ≥1, find f¹(x) and state its domain and range.

A: Given problem:- If fx=x-1 is now restricted to domain x≥1, find f-1x and state its domain and range

Q: JENCES AND SERIES: onvergent or divergent and, if convergen 23 an 20 ,n=1,2,3,...

A: The answer is given below:

Q: Determine the limits of the following Limit/ 1-c05 (22²) Ayo sinx

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Q: Find the equation of the tangent line to the curve y = 4x cos x at the point (, - 4). The equation…

A: