Question 2 Consider f(x) = 1/x on (0, 0). Show that for any a E (0, ∞0), the area of the triangle formed by the tangent line to ƒ at a and the positive x- and y-axes is constant.

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Q: Question 7 2²e"² sin(x²yz) Let f(x, y, z) 12 find dyəzə"x at the point (3, 0,0) 4 8.

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Q: An equation of the tangent line to the graph of f(æ) = (e¯")² at a = - In 2 is Select one: O a. y +…

A: As per company's norm we are allowed to solve only one question at a time. Repost the rest question…

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Q: QUESTION NO 1: Check the differentiability of the Heaviside function at t=0 t >0 H(t)=0 ift < 0

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A: F(x,y)=3 sin x - 7 cos y at ( 0 , π/2)

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Q: Question 7 Determine if h (z) = –- is continuous at x = 1. (Show your solution at your bond paper.)…

A: hx=x-1x2-1

Q: Question 28 Sin(1) – - -5 The Differentiation of f (t) =- 1+ 5t is- In(t) [In(1)]² A True B) False

A: f(t) = (1 +5t)/ lnt f'(t) = (5ln(t) - (1+5t)(1/t))/(ln(t))2 f'(t) = (5ln(t) - 1/t - 5)/(ln(t))2 so…

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Q: 10. a. Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the functions:…

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Q: Question 2 Consider f(x) = 1/x on (0, 0). Show that for any a e (0, o0), the area of the triangle…

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A: Consider the following function f(t)=2cost+sin(2t)Differentiate wrt "t"f't=2sint+cos2t⋅…

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Q: b. b-a Use the equation fte)dx = lim ** ) to evaluate the following definite integral. n-0k=1 2 |(2x…

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A: Linearisation of f(X) at a is given by-  L(X) = f(a) + f'(a)(x-a)

Q: Question 15. Obtain the following integral: I = f 3x? In(2x) dx as a function of æ to within an…

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Q: Question 4. Show that the average value of f(x) ei. = e- + cos x on the interval [-7/2,0] is

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Q: Question 8 In(t2 + e2)- 2 lim t 0 (a) 0 (b) 1 (c) 1/2 (d) 2 (e) none of these Question 9 The slope…

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Q: 16. If g(x) = x + 2 cos x, then the equation of the tangent line to the graph of g at x = is 3π 2 A.…

A: This is a basic application of derivative problem

Q: Question 3 If f(x) = f A sec ³x 1+elanx B 1+tan²x 1+etanx In (secx) √ 1+tan²x C tanx 1 + e sec²x D…

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Q: Question 14 Let z(t) be the solution to the following initial value problem (IVP) = (7z - 3)(2z –…

A: Consider the provided question,

Q: Find an equation of the tangent line at the given point on the curve. (a) x = 2 – 3 cos 0, y = 3+2…

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Q: Problem 3 Use part I of the Fundamental Theorem of Calculus to find the derivative of…

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Q: QUESTION 2 Use the definition of differentiability to show that the function f(x, y) = cos(x² + xy)…

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Q: QUESTION 2 Determine a potential function for F(x,y,z) = sin(y)e³²i - xsin(y)e?j + 3xcos(y)e32k or…

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Q: - [² Suppose F(x)= = sin(t) dt. Use the Fundamental of Theorem of Calculus to calculate - (F(x³)).…

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Q: The positive value of x at which the graph of y=1/x has a tangent line parallel to 4y= -x+3 O 1 O 2…

A: To find the slope of the tangent line to the graph of y=1x, differentiate the function, with respect…

Q: 1. The slope of the tangent line for the function f (x) = In x at x = 1 is: (A) (B) 1 (C) 0 (D) None…

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Q: let a>o be a fixed real number. Let acoscx?3+ X ln cy) = y2+2xy+ & -1 find the equation of the…

A: the given equation of the curve is: a2cosx2+xlny=y2+2xy+a2-1 we have to find the equation of the…

Q: Suppose f and f' are differentiable functions of r. Given f' (=) = 0, f" (4) = -1, and g(x) = log…

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Q: Question 8 Let f (x, y, z) : = xz cos(y). Find the directional derivative of f at (1,0, 2) in the…

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Q: Question 26 What is the maximum value of f(t) = sin t + cos t in the interval 0 <t < /2 O 2/2 O 2 O…

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Q: Question 3 Consider the function f(r, y) = 2x + 4y² %3D and the curve y(t) = (sin t, cos t), te…

A: Introduction: For a given function fx,y and a curve rt=xt,yt, their composition is frt=fxt,yt. The…

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Q: 7) Let x = t – sin(t) , y = 1– cos(t). Determine the equation of the line tangent at t = n.

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Q: Pls help

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