Question 8 x2 + 64 Using trigonometric substitution, given - dx, the simplified form of the integral is: sec³ede tan?e T True False

Q: olve the following Initial Value Problem: y" + y-6y 0, y(0) = 2 y (0) = -1. and %3D %3D %3D

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Q: 1.5 3-y Q1) Evaluate the integral dx dy

A: To evaluate the given integral.

Q: Q3) Evaluate triple integral y(x2 -y?)dz dx dy.

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Q: find the rational number represented by the repeating decimal. 0.451141414

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Q: Q2/ Fit a second -order polynomial to the data in the following table: 5 1 4 2 Y 2 8 3 4 -1 4 6.

A: We need to find quadratic equation.

Q: Evaluate the following and post your answers in t (Activity 2.1) 1.Sdz 2. Sa dx 3. S(7y6 + 8y3 –…

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Q: Evaluate (s 2 ds Oa.2 sln2-1) (In2)2

A: ∫ s· 2sds=2ssln2-∫2sln2ds=2ssln2-2sln22Add a constant to the solution=2ssln2-2sln22+C

Q: The global maximum of f(x) = x-4x over the interval -2sx<3 occurs at what value of x? O a. X = 3 O…

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Q: IVy+1-2dy can be evaluated conveniently if we let x =VVy+1-2 and dy = 4x(x² +2)dx. T True F False

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Q: Q1/ Estimate f (1.72) from the given data using Newton's Backward Difference Formula: 1.7 1.8 1.9…

A: we will use newton backward difference formula .

Q: Evaluate the following integral using Partial Fractions Method: x3 + x? y = dx %3D x2 + x – 2

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Q: Evaluate: | sech[In cosx]tanx dx A -2 tan -1(e cosx) +C В -2 tan -1(cosx) +C 2 tan -(ecosx) + C (D 2…

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Q: Find the value of t for which 1 V3x+1 O none of the choices 6 O 3 O 5 O 4

A: Here, given that: ∫1t13x+1dx=43

Q: d d. Calculate ri(t) · r2(t)] and [ri(t) x r2(t)] first by differentiating dt dt the product…

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Q: Q2) Convert the polar functionr= tan20 to cartesian.

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Q: Check the continuity of the function f(x). Explain why f(x) is continuous or not. x+1 =,x x2X > 1

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Q: Q5) Find volume of body bounded by z² + y² + x² = 9.

A: Explanation of the answer is as follows

Q: Given In.ry+x+ y =2. Find dy by implicit differentiation. dx

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Q: II. Multiple Choice: Read and understand the statements, then choose the correct answer. - Write the…

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Q: If a ball is given a push so that it has an initial velocity of 24 ft/sec down a certain inclined…

A: Given problem:- If a ball is given a push so that it has an initial velocity of 24 ft/sec down a…

Q: Find the value of x such that x satisfies the mean-value theorem at the interval [0. 1] for the…

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Q: (e) Suppose that the functionf is represented by the power series f (x) =1- +(-1)*. - -- +... 2 4 8.…

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Q: Question 13 - [x²/25+ x²dx , we let x= 5sine. (T True F False

A: We have to find integration

Q: Solve the following Initial Value Problem: y"+ 16y 0, x)= 2 and y'() = 5. %3D

A: Topic = Differential equation

Q: Find the value of x such that x satisfies the mean-value theorem at the interval [0. 1] for the…

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Q: DO NOT include spaces in between characters. And, DO NOT include dy/dx in your answer. Given In…

A: A detailed solution is given below

Q: Determine an antiderivative, y, of the given derivative, y. Then use the given condition on y to…

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Q: Evaluate the following integral using Trigonometric Substitutions Method: 1- x dx y =

A: Let's find.

Q: 00 sinde 2ode Estimate the slope of the tangent line. (b) what are the.units of measure for the…

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Q: a. f(x) = 4x + 11 find: f'(-2) b. f(x) = 2x2-5x 3 find: f'(2)

A: Given: f(x)=4x+11 f(x)=2x2-5x-3

Q: Consider the parametric curve defined by x=3+5t and y=1+31 Over which values of , does the curve has…

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Q: Find the derivative of the function f)= [sec() 6 sec-1 xVx2-9 1 sec x Vx2 -9 O 3 sec-G) 3. xVx2 -9 3…

A: In this question we have to find the derivative of the given function.

Q: Describe the graph of the equation. r = 18 cos ti + 4 sin tj -k O Itis an ellipse in the x = -1…

A: Let's find.

Q: Calculate ri(t) · r2(t)] and ri(t) x r2(t)] first by differentiating dt the product directly and…

A: =&gt; i have provided this answer with dull description in step-2.

Q: Suppose that y, denotes a nontrivial solution of the following second-order differential equation:…

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Q: The general solution of the second-order linear homogeneous differential equation y" +6 y=0 is y=…

A: Let's find.

Q: Describe the largest set S on which it is correct to say that f is continuous хx* + ху — 5 а. f(х,…

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Q: Which of the following yields the value 318? 3 (8х + 7у) dxdy 0 °0 (8x + 7y) dydx 0 °0 none of the…

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Q: Find an equation of the sphere whose diameter is the line segment having endpoints at (6,2, –5)

A: To find the equation of sphere.

Q: Evaluate: e* cos (7e*)cos (4e*) dx (A sin (3e*) +sin (11e") +c - sin (11e*)+C - sin 6. 22 ® -cos…

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Q: "u,V.w are three vectors such that each is incined at an angle of 4 with the other two, and that lul…

A: To find the scalar product of two vectors with the given conditions.

Q: 25-x2 In dx , if we letu=V25-x² , then udu= – xdx.

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Q: 9x 4. J, 16+9x

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Q: Consider the parametric curve defined by 1=3+5t and y=1+3 Over which values of doesthe curve has a…

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Q: dx = x +C 3. 45x dx = -5x +C 4. 12V dx =-x+2x' +C 4x + 35x 4. 4 +8x dx = -5xi +C 4 28x 15x dx = 4x+-…

A: The integration of the integral  35x3/4/4 +8x-3.

Q: Find dy dx I-Ln(x+3)=tかが(x:)

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Q: 3. Given the functions f (x) = a? - 4, g (x) = Va+ 4, and h (a) = %3D %3D | x + 2 find the DOMAIN of…

A: Domain is the set of all values  for which the function is defined.

Q: The graph of a function f is shown below. YA f a Graph b 1. Which grap is an antiderivative of f?

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Q: Q2 Find the limits 1- lim h +h cosh thcosh Sinh.cosh J4ズ メラ 2x-8

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Q: Let f be the function defined by ƒ (x) = cos( (/T). (a) Approximate the definite integral| f(x) dx…

A: We have to find the definite integral by using midpoint riemann sum and trapezoidal rule