Find the curvature of the space curve 9) r(t) = (t + 4)i + 4j + (In(sec t) + 7)k

Q: Find the critical numbers of the function f(x)=12x^5+45x^4-100x^3+7 and classify them. Round your…

A: The critical numbers of the function are x = 0,  x=2−3+29​​​​ or x ≈ 1.193 , and x=2−3−29​​ or x ≈…

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Q: 4. Mixing Concentrations (Differential Equations) Consider a one-litre tank filled with a saline…

A: The objective of this problem is to find the mass of the salt in the tank and the concentration of…

Q: Please can you help me witht he diferential geometry question I'm finding quite difficult

A: Step 1: Step 2: Step 3: Step 4:

Q: fors √2-6

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Q: -√x [3] (a) Evaluate dx √x (b) Determine if the following integrals are convergent or divergent.…

A: (a) To evaluate (b) To determine whether the following integrals are convergent or divergent.To…

Q: Let a and b be positive numbers with a>b. Let a1 be their arithmetic mean and b1 their geometric…

A: Answerhamdwritten  an+2 nt1 n+2 on,we pm">

Q: 4  For the function shown in the​ graph, give the​ interval(s) where the rate of change of​ f(x)…

A: Step 1:a) The rate of change is positive on the interval where the slope is increasing. From the…

Q: show all steps please! thank you!

A: The slope of the tangent line at point (x,y) is given as

Q: A ball is thrown into the air and its position is given by ℎ(t)=-6.7t^2+70t+11 where ℎ is the height…

A: Maximum height =6712987​ meters Time =67350​Explanation:Approach to solving the question: Detailed…

Q: Find the linear approximation to the following function at the given point 2 f(x)=-3x-4x; a = 3

A: GivenThe function and the value of a=3.The expression for the linear approximation is given byTo…

Q: Given csc(x)=-3 with 270° < x < 360°. Find cos(2x). о 2√2 1 3 - о 61 68 о 01 O-2

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Q: When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are…

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A: The final answer is:x=−2,y=−9,z=1Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Q1 C7

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Q: This is the curve sketching unit in calculus so show proper work and get correct answer

A: If you have any problem let me know here in comment box for this thankyou.

Q: Let y(x)=3 Estimate the slope of the tangent line of y(x) at the point x = 2: nonzero numbers after…

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Q: 1. Circumference of a circle: Consider the polar equation r = 2Rsine. Sketch the graph, identify the…

A: 1. Circumference of a circle.

Q: Find the slope of the tangent line to the polar curve r=4-5cos(theta) at theta = pi/3

A: If you have any questions let me know in comment box thankyou for your question.

Q: Find all local extrema using the second derivative test. Show all work for full credit. Make sure to…

A: 1. f(x)=9x5−9x3f(x) has a local minimum at x=53​​​​ because f′′(x)&gt;0.f(x) has a local maximum at…

Q: Calculate the average rate of change of the given function over the given interval. Where…

A: The objective of this question is to find the average rate of change of the function f(x) = x^2 - 3…

Q: Let аз +-(633) A and suppose that det A = 8. Determine det B if b3 B = a15c1a2+5c2 a3 +5c3 -3c1 -3c2…

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Q: Consider the function f(x)=10 root x +10 on the interval [2,5]. Find the average or mean slope of…

A: Therefore, the required answers are a) The average slope is m=310​(5​−2​)=2.739514717088982158b)…

Q: Use undetermined coefficients to guess the particular solution for y"-2y+5y= et sin(2t). Use A and B…

A: By using method of undetermined coefficients to guess the particular solution for the following…

Q: R 2) Evaluate the double integral ff (x² + y²) dA over the region bound by 9 ≤ x² + y² ≤ 25 by…

A: The objective of this question is to evaluate the double integral of the function (x² + y²) over a…

Q: A 500-gallon tank contains liquid that is 10% alcohol (the tank is full). A 50% alcohol liquid…

A: Step 1: Step 2: Step 3: Step 4:

Q: Find the length of the curve x(t) = e³t cos(t), y 3t = et sin(t) for 0 <t< Give an exact answer,…

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Q: 4.

A: The answers are as follows: a.   A=[−23​−21​​−1−21​​]. b.…

Q: (4) Find the equation of the plane tangent to the surface √√x²-yz = 1 at the point (3,2,4) Explain…

A: The answer is given below.Explanation:

Q: Let g be the function given by g(x) = x²ex, where k is a constant. For what value of k does g have a…

A: A real-valued function  f(x) of one variable x has a critical point at x=a , if the function is not…

Q: Let f be defined as follows. y = f(x) = x² - 3x (a) Find the average rate of change of y with…

A: given function

Q: Please solve the following calclus 3 problem: show all work by hand and follow all the steps.

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Q: A baseball team plays in a stadium that holds 46000 spectators. With the ticket price at $10 the…

A: Given points: (10, 19000) and (9, 23000)Calculate slope m: (23000−19000)​/9-10=−4000Use slope m and…

Q: Find the average rate of change for the following function. 2 f(x)=5x³-3x² + 2 between x = -2 and x…

A:

Q: Determine whether the sequence converges or diverges, if it converges, find the limit.  an= e-1/√n

A:

Q: 1. Given the below graph of f(x) = f(x) = x2 x-2 a. As x-co, f(x)→ b. As x 2, f(x)→ x 3 4 5 6-7 C.…

A: We need to determine the values of f(x).

Q: 3 1 -2 3 A = B = 02 -1 10 -20 4 -1] -22 calculate (if possible): a)-3AT+2B Instructions for the…

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Q: Q4 C7

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Q: Find the curvature of the curve (t) = = (3 cos(2t), 3 sin(2t), 3t) at the point t = 0 Give your…

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Q: Find the average rate of change for the following function. f(x)=5x³-3x²+2 between x = -2 and x = 3…

A: The formula for the average rate of change is: Average rate of change=b−af(b)−f(a)​ Where: a is the…

Q: Find the unit vectors that are parallel to the tangent line to the parabola y = x² at the point (6,…

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Q: 20. Given that f(0) = 12 and following graph, write the formula for a polynomial func- tion of least…

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Q: Annual sales of fountain pens in Littleville are 8,000 per year and are increasing by 9% per year.…

A: The annual sales of fountain pens are 8000 per year It is increasing at a rate of r=9%

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Q: Let y = sin(4x). If ▲x = 0.2 at x = 0, use linear approximation estimate Ay Ay≈ = Find the…

A: The given function is  and

Q: Find the first four terms of the Taylor series for the function 2 tan(x) about x = П 4

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Q: y= -3 Cos (2π - 5x ) -1 , determine : • period , amplitude, range • three maxima • four minima…

A: Please see the attached images for a full solution. Thanks.Explanation:

Q: Consider the function f(x)=1/x on the interval [1,11]. Find the average or mean slope of the…

A: The objective of this question is to find the average slope of the function f(x)=1/x on the interval…

Q: Ay 15 12 9 Solve graphically by the intersection method. Give the solution in interval notation.…

A: The objective of this question is to find the point of intersection of the two given lines y₁ =7x+…

Q: Use algebra and the properties of limits as needed to find the given limit. If the limit does not…

A: