Given the function f(x) √x f(x) = COS 2 1 + √r dr Determine the instantaneous rate of change at x = 1.|

Q: π 2 EK 4 cot4 x dx

A: Here, note that: ∫cot4x dx=∫cot2x cot2x dx=∫(cosec2x-1) cot2x dx=∫cosec2x cot2x dx-∫cot2x…

Q: It is projected that the population of a certain town will be P(t) = 2t+4+³/2 + 5000 where P(t) is…

A: Rate of increase of population=P(9)-P(0)9-0

Q: Answer

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Q: If (2, 1) is a critical point of f and fzz(2,1)ƒyy(2, 1) < [ƒzy(2, 1)]², then ƒ has a saddle point…

A: Here, the given statement is: If (2,1) is a critical point of f and fxx(2,1)fyy(2,1)&lt;fxy(2,1)2…

Q: What is the integral of (2 sec^2x - sinx) dx? * O 2 cosx+tanx + C 2 tanx + sinx + C 2 tanx + cosx+C…

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Q: Find the equation of the line tangent to y = e The equation of the line tangent is y= at x = 1 - In…

A: Given query is to find the equation of the tangent.

Q: Let w = (2, − 1, 1), v = (− 4, − 5, 1), and u = (6, − 2, 2). Find u × (v × w)

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Q: What is the y = x^2 - 4 and x-coordinate of the centroid of the plane region bounded by y = 2x - x^2…

A: Here we have to find the x coordinate of the centroid of the area bounded by the curves.

Q: The function f(x) = 900 represents the rate of flow of money in dollars per year. Assume a 10-year…

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Q: The function defined by y=√-² has as its graph a semicircle of radius r with center at (0.0) (as…

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Q: I. Directions: Determine if the function is continuous on the given interval 1-3. f(x) 2 12-x² ; [1,…

A: 1. fx=212-x2; 1,32. fx=2-x+3; -3,-13. fx=1if x≤2x2-3if x&gt;2; 2,4

Q: What is the volume in cubic units of the solid formed when the region bounded by y = x^3, y- axis,…

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Q: Let f(x, y) = (x³ − x)(y² – 1). Find fry(x, y).

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Q: Find the volume generated if the area between y = coshx and x- axis from x = 0 to x = 1 is resolved…

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Q: 3. Find f'(x) if f(x)= 3 2x + sin r

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Q: 1. Why is it important to use the six trigonometric ratios in getting a missing angle value?

A: The six trigonometric ratios are sine, cosine, tangent, cotangent, secant, and cosecant. Basically,…

Q: Evaluate the integral: 1 - coth² (log₂ x) S² x cosh(log₂ x) dx

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Q: Find the area bounded by the curve x = y² + 2y and the line x = 3.

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Q: Evaluate the limits using the L'Hopital's Rule. lim (tan x) (sin x-1) x+2+

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Q: ∙1 Ꮭ ᏝᎽ 1-x-y z dz dy dx

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Q: 5. Find the area bounded by y = sin √x and y = 0 on the interval [0, π²].

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Q: 8. Find the area of the region in the first quadrant bounded by the curves y = sin x, y = cos x and…

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Q: Evaluate the limits using the L'Hopital's Rule. lim (tan x)(sin x- x-1) x+2+

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Q: 4 -dx converges or diverges, and find the value if it converges. Determine whether the improper…

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Q: Let h(x) = f(x) = g(x). If f(x) = 9x² and g(x) = 8x, what is h'(-5)? - Do not include "h' (-5) =" in…

A: SOLUTION-

Q: Determine the intervals on which the function is concave up or down and find the points of…

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Q: II. Evaluate the following integrals. 4. J 9x² 9x → 5 - 18x + 13 - dx

A: A detailed solution is given below.

Q: 22. =2x²-3x+1 at (-1, 6)

A: Topic = Derivative As per guidelines , At a time only one question can be answered. please repost…

Q: 2. lim (x - Inx)* x)² 2-0+

A: Here, the given limit is: limx→0+(x-ln x)x which is (-∞)0 form.

Q: The following differential equation is a Bernoulli equation: 2 dy + 27/ y3 where y = f(t) dt By…

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Q: - 4. Find the area bounded by y = x - x² and y = x(x − 2)(x+2).

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Q: A real estate firm estimates that the value of a certain property will be given by the function V…

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Q: Given that sin(0)= TT 3 and 2 <0<π what is the exact value of cos(20)?

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Q: Evaluate f(x³ - x + 1) dx a. 0.250 b. 0.500 c. 0.625 d. 0.750 e. NONE OF THE ABOVE

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Q: FIND X: 6.95460 = -0.658 + 1.41853 + 9.36 (log10 (X + 1)) + 0.40+ -0.20091 1094 (X+1)5.19

A: Given:  6.95460=-0.658+1.41853+9.36log10x+1 + -0.200910.40+1094x+15.196.19407=9.36log10x+1 +…

Q: Use the Second Derivative Test to find all relative extrema. h(t) = -x + 6x² - 4

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Q: 2x x→∞ 3x² +5 3x xx√√√x² x² +4 X lim x→→∞ 2 sin î (a) lim (b) lim (c)

A: Given

Q: 3. |2 – 2" | da - 22

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Q: -.f x³ ex² dx 3

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Q: Find an equation for the hyperbola that satisfies the given conditions. Foci: (0, ±7), vertices: (0,…

A: We have to solve above hypobola question

Q: Use the Second Derivative Test to find all relative extrema. (a) h (x) = x - 2 cos x, [0, 4π]

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Q: 3. Water is flowing into a vertical cylindrical tank at the rate of 24 cubic ft. /min. if the radius…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: II. Find the value(s) of x (or the interval of convergence) 2. Σn=0 for each of the following power…

A: The power series is  ∑n=0∞ (-1)n+1(x-5)nn·5n

Q: For the function defined as follows, find all values of x and y such that both fx(x,y) = 0 and fy…

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Q: A particle moves in a straight line from the origin (at t= 0) with given initial velocity u, and…

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Q: Test for exactness, then solve.  ey dx + (2y + xey) dy = 0

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

Q: two iterat x' = -2x+t, using successive approximation. x(0) = 1.

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Q: 14. Find a function whose tangent has slope 4x+1 for each value of x and whose graph passes through…

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Q: 8. A company is selling calculators for $100 each. How many should it sell to break even if it costs…

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Q: 6. y dy 1+√√y 11

A: SOLUTION-