Determine the antiderivatives of the following functions: 4. f(3x² +1)4 x dx 5. s dx

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A: This question can be solved using the concept of properties of definite integrals.

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Q: 3.y" + 6y + 8y Pros Зе 2х + 2x

A: Let's solve given diffrential equation.

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A: This question can be solved using the concept of increasing and decreasing function.

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Q: Q1/ find the Eigen value and Eigen vector for the largest Eigen value if -2 2 -31 [A]= 2 1 -6 -1 -2…

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Q: Use Taylor's Theorem to find an interval [ z, z] where the Maclaurin polynomial p2(x) = 1- 2 1…

A: Given problem  is :

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Q: A poster of area 6000 cm² has blank margins of 10 cm wide on the top and bottom and 6 cm wide on the…

A: A poster of area 6000 cm2 has blank margins of 10cm wide on top and bottom and 6cm wide on the…

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Q: Q1: If the function f(x) define as f: R →R such that f(x)= (x+1, x>2 x²-1, x≤2 Show that the…

A: Solution is given below:

Q: Q2: (A) Show that if y=csc(u), then dy -csc(u) cot(u) du dx

A: I have stated the used formula in the solution

Q: . Determine the area below f(x) = 8x - 2x² and above the x-axis.

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Q: The arc length of y=In(cos x), 0<x<• is 3 ○A In (√2-1) A. ○ B. In (1+√3) C. In (2+√√3) D. In…

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Q: 4. find the given general differential solution, using homogeneous equations with constant…

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Q: f(-7 sinx + 3cosx)dx 4

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Q: Determine whether the given function is even, or odd, or neither. One period is defined for the…

A: Odd function        f(x) = -f(x)     for all xEven function        f(x) = f(x)     for all xIf…

Q: Which of the following is not an indeterminate form? * ∞-∞ O Option 1 0/0 O Option 2 1∞ 1/0

A: Topic = Limits Correct option = 4

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Q: (B) What function f(t) has Laplace transform: f(s)= s² + 1 s(s+s-12) 12

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A: We have to find derivative

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Q: ntegral sydx 2. ] [ -1-1 (x + y + 1)dxdy

A: As per our norms we have to write one question at a time kindly repost remaining questions

Q: Q 19 If a fault cuts three sides of a quadrilateral, then: Red with one of the vertices 2- Cut the…

A: Given question:- 19) if a fault cuts three sides of a quadrilateral then,

Q: Let F be the function below (Click on graph to enlarge) Evaluate the following expressions. Note:…

A: limx→a F(x)=L if and only if limx→a+ F(x) = L= limx→a- F(x) . A function F(x) is continuous at x=a…

Q: Use false position method find the diameter (D) of the pipe which satisfies the follow ation:…

A: answer is in next step

Q: Carbon Monoxide Pollution The number of cars running in the business district of a town at time t is…

A: topic - composite functions

Q: Question 8 (a) Find the following integrals: 1 (1) √4x²+0 d 6 (ii) -dx -2x-8

A: (i). Given: I=∫14x2+9dx   ...1   As we know that; The trigonometric identity; 1). tan2x+1=sec2x 2).…

Q: Part II. Calculating Second Order Partial Derivatives. Find all the second order partial derivatives…

A: Note : As per our guidelines we are supposed to answer only 3 subparts if there are multiple subpart…

Q: Find the tangential and normal components of the acceleration vector at the given point.…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: The graph shown is f(x) = 1⁄x². Y 5 4+ 3 2+ 1 + 54 3-2-11 1 2 3 4 5 -2 -3- 4 -5 X If g(x) = f* f(t)…

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Q: (b) Find the dimensions of a box with a square base with surface area 20 and the maximal volume. Use…

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Q: Determine whether the given function is even, or odd, or neither. One period is defined for the…

A: We have to find if the function is even or odd.

Q: T (3 sec² x + 4 csc² x) dx 3

A: The given integral,        ∫π3π43sec2x+4csc2xdx