Differential Equation d²y dx² 1) d³ y dy dx3 dx 2) (D³ + 3D² 4D - 12) y 3) 2D4 +11D³ + 18D² + 4D 8 = 0 = = Auxiliary Equation O(A) (D) (G) Roots (B) (E) (H) General Solution (C) (F) 1)

Q: Find the derivative dy dx dx of the function y = sec (1 + 4 + sin ¹(4 + ²)

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Q: Let g(x) be the inverse function to the differentiable function f(x). If f(0) = 1 and f'(0) = 8,…

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Q: Find the distance between the points. 2 (3, 3), (3, -1) 2 units

A: To find the distance between given to points.

Q: 9. At 2:00 PM a thermometer reading 80°F is taken outside where the air temperature is 20°F. At 2:03…

A: Given problem:- 9. At 2:00 PM, a thermometer reading 80°F is taken outside where the air temperature…

Q: 6. Evaluate the following multiple integrals. π +2 (a) y sin(xy)dady (b) [1² fr esc² 0dødr π/4 π/2 ©…

A: As per our guideline we have to solve only first three parts

Q: Find the derivative of the trigonometric function. Use the chain rule. f(t) = 5 sec9(pi(t) − 4)

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Q: Given the differential equation xy³dx + (x²y² + 1) dy = 0, What is SN dx ?

A: We are asked to find the δNδx

Q: Let g(x) be the inverse function to the differentiable function f(x). If f(0) = 1 and ƒ'(0) = 8,…

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Q: Calculate the derivative. ƒ"(1), f(t) = 15t t+1

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Q: Find the derivative of each of the following functions:- log₂ x 2. y=- X

A: The given data is: y=log2(x)x   To find the derivative.

Q: X hat is the value of lima f(a)-aƒ(x)? r-a

A: Topic:- limits

Q: a) ㅠ 3 cos x sinx dx

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Q: Let R be the region enclosed by the curves y = x³ and y = 2x². The area of R using vertical element…

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Q: Consider a plate (the plate has the same shape as the region enclosed by y = x² and y = 4) submerged…

A: We need to find a, b.

Q: Use the table of integrals to evaluate the integral. (Use C for the constant of integration.) 25x² +…

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Q: You've been asked to calculate the mass of a conical pile of sawdust measuring 7 meters high with a…

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Q: 13 X ƒ(x) = [5,-3],ƒ(c) = -1/ x²-4,

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Q: The function f(x) = √√x-2 + √√4-x is. increasing on its natural domain O increasing on (2, 3) and…

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Q: Let f(x) = 8x²(x-2) + 15. Find the critical points c that correspond to local minima. (Use symbolic…

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Q: £₁₂ √x (4-x) elx

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Q: Q1:- A. Solve the following differential equatic 1. dx = (1 + y²)ex

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Q: Prove lim-13x+2=-1

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Q: Compute the following limits, if possible. You may use L'Hospital's (Bernoulli's) rule if it…

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Q: √y² +9 dy 4 X using reciprocal substitution

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Q: Verify that f has an inverse function. Then use the function f and the given real number a to find…

A: The given function f(x)=x-9, x>9

Q: Evaluate x² + y² 1 x² + y² + 16 in the first octant. JJJ₂₂ dV, where E lies between the spheres x² +…

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Q: Find the derivative dy dx || dy dx of the function y = sec (₁ +√4+ sin ¹(4 + ²))

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Q: The figure shows f, f', and f". Determine which is which. 7 The graph of fis O graph 3. graph 2. O…

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Q: Find the distance between the points. (Round your answer to two decimal places.) (9.1, −2.6),…

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Q: Exercise 15.5.1 Evaluate the triple integral * "** (rz sin 0)r dz dr de. =0 Hint 8 X

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Q: S x² √x²+4 dx

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Q: Find the Jacobian of the transformation z = 4u – 6v, y = u² − 2v

A: The objective of the question is determine the jacobian transformation.

Q: ? Question Classify the critical points of h(x, y) = x²y + xy² + x³y² + xy³ found in the previous…

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Q: Find the volume of the parallelepiped whose edges are represented by A=î-13j+ 4k, B = 3i+2j-7k and C…

A: This question is related to volume of parallelepiped, we will solve it using it using given…

Q: Give 1 problem for differentiation rule of exponential

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Q: magnitude of vector BC |BC| = magnitude of vector AB | A B|= angle A (using dot product) angle B…

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Q: Evaluate cos √6x dx using a substitution followed by integration by parts.

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Q: Problem 1: A force of 500 dynes stretches a spring from its natural length of 20 cm to a length of…

A: Concept: Work done by integration: W=∫x=abf(x)dx Where W represents work Force is represented as a…

Q: (c) Given the following second-order differential equation d²y 2 +7y-3x²=5 dx² Find the general…

A: We have to find the solution of the given differential equation.

Q: Find the x-value of all points where the function below has any relative extrema. Find the value(s)…

A: Solution is here

Q: Suppose that f(x) is differentiable for x > 0, y = 2x + 1 is the tangent line to the graph of f at x…

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Q: II ex elx е ех его

A: Given

Q: Find the derivative of the trigonometric function. y = cos((?x)8)

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Q: Let g(x) be the inverse function to the differentiable function f(x). If f(0) = 1 and f'(0) = 8,…

A: Given g(x) is the inverse function of f(x)

Q: C. Evaluate the following: i(z³+1³) 1. lim 24-1 2²+1

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Q: Find the center of mass of a lamina as pictured below, with inner radius 3 and outer radius 5, with…

A: Given problem:-

Q: (a) Any critical point of a function f is either a local maximum or local minimum for f. True False…

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Q: 2 Find the volume of the parallelepiped whose edges are represented by A =î - 13ĵ+ 4k, B = 3î+ 2j-7k…

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Q: 4. (ази t эзо

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Q: 5. A ball of mass 2 kg is dropped from rest in a viscous fluid, the resistance of which is 0.001v N…

A: By solving differential equation