The normal vector of x+2y-1-0 (0, 2) (2, -1) (1, 2) O (1, -1)

Q: Use differentials and the graph off to approximate the following. (Round your answers to three…

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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: 10 times as many as 1 hundred is_______ hundreds or ________ thousand

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Q: 3 If f(x) = 2 + x, evaluate Σƒ (k+1). atas (k k=1

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Q: If f(x) = f'(x) = 4-3x7, find f'(x). Use exact values.

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Q: Find the inflexion point(s) of f(x) = x²-3x²³

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Q: Solve the differential equation (2x + y) dx (4x + 2y − 1) dy = 0 O a. 5x 10y + In 10x 5y 2|= C O b.…

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Q: Find the average value of the function over the given interval. (Round your answer to three decimal…

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Q: Find the slope of the tangent line to the curve − 3x² + 2xy − 4y³ at the point (4, 1). - 44

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Q: If 2x² + 3x + xy = 3 and y(3) = — 8, find y' (3) by implicit differentiatio

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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: Imagine you want to enclose a field in the shape of a rectangle with a semicircle on one end. If you…

A: Imagine you want to enclose a field in the shape of a rectangle with a semicircle on one end. If you…

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

A: #10

Q: Evaluate the integral using the following values. [x³ dx = 260, x 29 - ·[³x dx = 10, [³dx = 2 (29 -…

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Q: 4) Activity 5: Check for Understanding (10 mins) NOV ob For the equation of y²dy = x(xdy - ydx)e*/y.…

A: We can find the degree of the given function and differential equations.

Q: Find the limit of s(n) as no - + [n(n+¹)] s(n) Submit Answer

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Q: 6) Line y=x between x = 0 and x = 1 is rotating around the x - axis. (It forms a cone). Calculate a)…

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Q: Find the following using the table below. Xx 1 2 3 4 f(x) 3 4 2 1 f'(x) 2 3 2 1 4 g(x) 2 3 1 4 g'(x)…

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Q: 2. If f: R→→ R satisfies f(1) = 3 and f'(x) ≥2 for all x's, how small can f(7) be?

A: Here we have to find the smallest value of f(7).

Q: Suppose that a population grows according to the unlimited growth model described by the…

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Q: Please correct me if i'm wrong. The points where f(x) appears to concave downward appears to be…

A: Given , the point where f(x) appears to be concave downward appears to be (-2 , 2.9 )

Q: Explain how the fundamental theorem of calculus relates integrals and derivatives. Formats T B T U…

A: Fundamental theorem of calculus relates integrals and derivatives.

Q: Which of the following is the correct limit definition for the derivative of g(x) = x² + x? O (x+h)²…

A: We have given function  gx=x2+x gx+h=x+h2+x+h Derivative of g(x) is given as  g'x=limh→0gx+h-gxh…

Q: dr Let A be the area of a circle with radius r. If dt = 4, find dA dt when r = 5.

A: Area of a Circle , A = πr2 ; where, 'r' is the radius of the circle .

Q: VIBDIC he following DES. to E visbiol

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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: f(x) = = -2x² + 7 7x - 10 if x -1

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Q: 1. Use the Mean Value theorem to show that for any two real numbers a and b, we have | sin b - sin a…

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Q: 2 -1 4 3 N у -1 1 2 X

A: Graph of the function is given, we have to find its domain and range

Q: Find the limit, if it exists. 4x² lim X--X+2

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Q: Consider the function f(x) = r? – 5 +4 x + 1 a. Find the first derivative. f'(x) = b. List any…

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Q: Which of the following is a possible equation for the following trigonometric function?

A: To find which of the given equation is possible equation for the trigonometric function.

Q: Find the length of the curve r(t) = Interactive 3D Graph (√2t, et, e-t) over the interval 0 ≤ t ≤ 1.…

A: The given curve rt=2t, et, e-t over the interval 0≤t≤1 To find the length of the curve on the given…

Q: 3. A ladder 10 feet long is leaning against the wall of a house. The base of the ladder is pulled…

A: Concept: Let x represent the distance from the wall to the ladder's base. and let y be the height of…

Q: A solution of the differential equation d²y dy +4- + 4y = 4e¯¹ dr2 da takes the value 1 when z = 0…

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Q: Find the Domain and Range of the function (Have your answers in interval notation)

A: Question: Find the Domain and Range of the function (Have your answers in interval notation)

Q: Consider the following function. f(x) = x² - 4x + 5 (a) Find the critical numbers of f. (Enter your…

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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: Question 6 Determine the Fourier series for the function defined below: f(x) = 2x in the range x = 0…

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Q: functions f (x) = 2 and g(x) = 1 (i) Consider the (a) Write down the domains of the functions f (x)…

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Q: Question 2 Determine the solution of the second-order differential equation: d²y dx 2 dy -7—+12y=e²³…

A: Ode

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Q: An internet bookstore charges $15 shipping for orders under $100 but provides free shipping $100 or…

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Q: You have an investment of $22,400.00 that you want to double in 11 years. If interest is compounded…

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Q: ve passes through the point (0, 9) and has the property that the slope of the curve at every point P…

A: Topic:- application of integration

Q: 14. 2y dx + x(x² In y − 1) dy = 0. -

A: To find the solution of the given differential equation.

Q: 6)Find the first quadrant area of the region bounded by curves defined by given equations

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Q: 5. dy/dx = sin(x + y). ANS. x+c = tan (x + y). sec (x + y).

A: Please see the below picture for detailed solution.