Let / be a twice differentiable function. One can show that e* (exf)" = af" + bf' + c, where a, b, c are constants. Here the double primes denote the second order derivative. Match the following. b Choose...

Q: Consider following ODES: 1)4y" +12y' +13y=0,2) 2y″ +7y' + 5y = 0 a) Find characteristic equation and…

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Q: Find the interval(s) on which ƒ(x) = |x² − 5x + 15 is differentiable. Enter your answer using…

A: The given function fx=x2-5x+15 We have to find the interval on which fx is differentiable.

Q: Show that the triangle with vertices A, B, and C is a right triangle. d(A, B)2 d(A, C)2 + d(B, C)² =…

A: Topic - Pythagoras theorem and area of a triangle We are given, three points on a triangle as…

Q: g(x) = 25x² (a) (¹) (b) (c) (d) 1 g(a) g(√a) ✓g(a) Additional Materials

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Q: X = 8 At the end of your work, sketch the graph of 5 x²¹ 2. y 8x8 and 1. y = 3. The tangent line at…

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Q: M3.2. d. A cadet engineer determines that when x hundreds of units of a particular commodity are…

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Q: e think of In(-3x + 7) as In(u), then u is a differentiable function of x and u = tionally, if we…

A: Topic:- application of derivatives

Q: Find y': y = arc cos 0 = -√2 O y Oy=-1/72 V Oy= Oy=-- 9-1² 3

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Q: Given a first-order differential equation: /1 + x² dy-ydx = 0 a) What is the best solution method in…

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Q: Consider the surface x² + y² - 2xy - x + 3y - z = 0 at the point Po(2, -3, 14). Determine the…

A: Concept: The equation of the tangent line at point x1,y1,z1 a(x-x1)+b(y-y1)+c(z-z1)=0 The symmetric…

Q: In getting the derivative of a variable raised to a variable y = [f(x)](2), which of the following…

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Q: Question 26 Find the second derivative (y") of the given function: y = e² sin z *)(2(- sin x)) e²…

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Q: Are 2 -baz

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Q: Find the area of the region bounded by the curves y = xe -0.4x Area = x = 5, and y = 0. >

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Q: Find the volume of the solid that lies under the hyperbolic paraboloid z = 3y2x2 + 4 and above the…

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Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: See this solution in below.

Q: b) Find the differential of the function f(x) = tan(√x)

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

A: Given thatthe table To find :1. h'2 if hx=fx.gx2. h'2 if hx=fxgxSolution…

Q: Find the parametric equation for the line where the planes 4x + 6y + 2z 12 and 2x - y + z = 2…

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Q: 5. (a) Find the directional derivative of f(x, y) = √√x² − y² at P(5,3) in the direction of v =…

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Q: Evaluate the integral 10 10 sin(x) cos(x) Note: Use an upper-case "C" for the constant of…

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Q: Find the directional derivative of f(x, y) = √xy at P(7, 7) in the direction from P to Q(3, 4). Duf…

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Q: y = 7 cos(x), y = 7 − 7 cos(x), 0 ≤ x ≤ π

A: Given y=7cosx, y=7-7cosx, 0≤x≤π

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Evaluate a multi-variable function Let f(x, y) = √√150 - 2x² – 4y², and evaluate f(1, 0). Please…

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Q: Evaluate the integral 1 Note: Use an upper-case "C" for the constant of integration. 9x² √4x - x² dx

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Q: xis that the terminal position of the angle resides in and state the value of the reference angle.…

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Q: Find the derivative. 1 y = _x3 + 3x + Væ 2 Ody dx O Ody dx || ip O 32 y=2x2 +3 + 2x 32 || 2 X +3+1/x…

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Q: tanh(lnx) = x² - 1 x² + 1 22

A: I am attaching image so that you understand each and every step.

Q: Finally, determine (x³. - x + 8) and simplify the result. Recall that multiplication is commutative…

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Q: What else do you observe? Concept Check: Evaluate the following integrals: 4. f 55 5sin2x *cos2x dx…

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Q: 81.2² 18 3x-2 = For the rational function h(x) a. Find any intercepts of the function. State them as…

A: to find the y-intercepts, take x=0

Q: The third derivative of the second derivative of y = f(x) is also O y(4) Oy (3) O f(5) (x) O D²y

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Q: The graphs of the function F (left, in blue) and G (right, in red) are below. Let P(x)=F(x)G(x) and…

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Q: Find an equation of the level curve of the function z(x, y) = ey (x² + y2) that passes through the…

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Q: f(x) = 2 sinxtx 3 2x + 6x + 2

A: Topic:- application of derivatives

Q: 9. A Rectangular box w/an open top is to be made from a square piece of cardboard that is Binche's…

A: This question can be solved using the concept of maxima and minima.

Q: A rectangular package to be sent by a postal service can have a maximum combined length and girth…

A: NOTE: Refresh your page if you can't see any equations. . x=side of the square cross-section of the…

Q: Find the integrating factor (3x²y-x²) dx + dy=0 Select one: 0 а. ex O b. O C. e-x² Od era O e.

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Q: Applications of Planes in Space Find the acute angle (in degrees) between the planes - 2x - 4y + 2z…

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Q: (a) d (√1+x²)

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the differential dy of the given function. (Use "dx" for dx.) y=x√√9-x² dy

A: find differential dy

Q: Find the derivative of y = 3x² − 2x + dy = 6x 2 dx dy dx dy dx Oy = = 3x - 1 = 3x - 2 6x - 2

A: Given query is to find the derivative of the function.

Q: 4. Find an equation of the tangent plane to the surface xy + yz+zx = 3 at the point (1,1,1).

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Q: The volume of a cube with sides of length s is given by V = s³. Find the rate of change of the…

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Q: Determine the derivative of the given function: y = e OV=11/1/20 y y = -6xe 7 y' = -2x-¹e-3/ 0 0y=…

A: To find the derivative of given function.

Q: Sketch the region enclosed by the given curves. Draw the approximating rectangle, label its height…

A: see below the figure of the region and rectangles that can be construct in the region.

Q: Use logarithmic differentiation to find the derivative of the function. y = (In(x)) cos(9x) y'(x) =…

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Q: Question 2 Let f(x, y) = 5e¹* sin(3y) af д х af dy =

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