1/2 S 5 sec²(x)tan(x) dx 0

Q: Consider the function below. In x 9√x (a) Find the interval on which f is increasing. (Enter your…

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Q: Convert the following standard form to general form of parabola. a. (y+1)²=-2(x+2)

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

Q: Find the intervals on which the graph of f is concave​ upward, the intervals on which the graph of f…

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Q: 16 Let Find A-1, if it exists. a) O b) O A|- A10 ú A/w Alu o N/W N/W - alt AI AI A Alo Alto ú -4 -|-…

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Q: 1. Evaluate the following integrals: 5/2 d. S3 1 1/2 2 2x -x -dx

A: The integral is  ∫1/25/2 12x3-x2dx

Q: If 0 satisfies the inequalities cos(0) 0, in which quadrant must 0 lie? 1. Quadrant III 2. Quadrant…

A: Given query is to find the correct quadrant for θ

Q: the deflection of differential equation shown 26. dy a d'y = w(x) on 0<x<l dxe" ·beam 9. y.(x)..…

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Q: 2. A 71.6m tower is to be constructed on a hill with a slope of 15.6°. Both cables make a 42.5°…

A: We will use sin Rule to find the length of each cable.

Q: Solve the following differential equation: [e2y − y cos(xy)]dx + [2xe2y − x cos(xy) + 2y]dy = 0

A: e2y − y cosxydx + 2xe2y − x cosxy + 2ydy = 0

Q: If y = x4 + 2x, find the values of delta y and dy when x = 2 and dx = 1

A: Please see the below picture for detailed solution.

Q: If 0 satisfies the inequalities sin (0) > 0, sin(0) cos(0) > 0, in which quadrant must lie? 1.…

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Q: 3) Consider the function G(x) = f g (t) dt. Find the derivative G' (x). O g(x) g(x)-g(1) O g(t) O…

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Q: (a) Using algebraic division and integration by substitution, or otherwise, show that - dx = e² −…

A: We can evaluate the given integral by using the substitution u = ex

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the funct 8 + sec(6t) dt…

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Q: Find a value of c so that f(x) is continuous at x = 1. f(x) = O c=1 O None of these Oc=0 ○ c= -1 O…

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Q: d (a) / ₁ (t²-1)²dt. -10 -10 (b)/(t²-1)²dt. (c) d dx 32² -10 3x² (t²-1)² dt. d (d) — (t²-1)²dt. dx…

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Q: Evaluate each expression using the graphs of y=f(x) and y=g(x) shown below. a) (gof)(6) b) (gof)(0)…

A: To find (fog)(a) = f(g(a)), first find g(a) . Then, put the value of g(a) in f(g(a)) . Let g(a) = b…

Q: 45. If F(x) = f(g(x)), where ƒ(−2) = 8, ƒ'(−2) = 4, ƒ'(5) = 3, g(5) = −2, and g′(5) = 6, find F'(5).

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Q: Evaluate the integral 9 3 12 SS S 00 4y 9 3 12 SSS 0 0 4y (Type an exact answer.) 3 cos (x²) 4√2 3…

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Q: Find the linear approximation to the function f(x) = 3x + 4 at a =3, [0,6].

A: Linear approximation formula f(x) = f(a) + ( x-a )f'(a) Given f(x) = 3x + 4

Q: Use linear approximation, i.e. the tangent line, to approximate 1.86 as follows: Let f(x) =X f(x) at…

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Q: Convert the general form to standard form of parabola

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Q: Find the linear approximation of f(x) = ln x at x = 1 and use it to estimate ln(1.4). L(x) =…

A: Given function:- fx=lnx

Q: Given the vectors u=-i-3j and w=-7i+5j, find -4u and u-w. Write your answers in the form ai+bj.

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Q: The region W lies below the surface f(z,y)-8e (3) and above the disk z² + y² ≤ 16 in the zy-plane.…

A: We have to find the area and volume integrals.

Q: Determine whether the integral is convergent or divergent. 3 36 √3-x O convergent O divergent dx If…

A: Given integral:- ∫23363-xdx

Q: (5) Determine if the alternating series converges Σ(-1)^n. 8 n=2

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Q: What is the rate of change of x with respect to y when the bottom of the ladder is 4 m away from the…

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Q: Question Three (a) Prove that F(x, y, z)= (y² cosa+z³)i+(2y sin a-4)j+(3rz+2)k is a conservative…

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Q: Use the Quotient Rule to compute: ਹੈ y dy y+5æ

A: By Quotient Rule ∂∂xuv=v∂u∂x-u∂v∂v2

Q: Test the series below for convergence using the Ratio Test. (-1)"62n+1 (2n + 1)! The limit of the…

A: The given series ∑n=0∞-1n62n+12n+1! We have to find the convergence of the series using the ratio…

Q: Atmospheric pressure P in pounds per square inch is represented by the formula P = 14.7e-0.21x,…

A: Given P = 14.7e-0.21xwhere P = atmospheric pressure in pouds per square inch x = number of miles…

Q: -4-x² - y² 4 component. For the function f(x, y) (-3, -3) that has a positive find a unit tangent…

A: Let's find unit tangent vector.

Q: Find sin 2x, cos 2x, and tan 2x if sinx = - sin 2x cos2x tan 2x = 11 0 0 2 √13 and X terminates in…

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Q: Let Give the 2,1 entry of 4-¹. a) 0-¹ b) 0¹/2 c) 03/2 d) 0-5 e) 0-2 f) O None of the above. 02 2 A-1…

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Q: Verify Green’s theorem in the plane for R C (3x 2 − 8y 2 ) dx + (4y − 6xy) dy, where C is the…

A: Given:

Q: Let f(x,y) = 2x^2 + xy −y^2. Prove that the directional derivative of f(x,y) at point x = (3,−2) in…

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Q: -G) ¹ + ¹ +)* 3 2 (f)_7(t)=e¹i+e¹j+t√2k for 0≤t≤1 (e) r(t)= k for 0≤t≤1

A: (e).The given vector function is:r→(t)=t33i→+t22j→+12k→          for   0≤t≤1

Q: 1. Find the derivatives of the following functions: a) f(x) = 2x³ + e²x b) f(x) = ln (2x - 1)5

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Q: 2 3 S (x+1)² 1 2 x +2x +x+2 -dx ₁

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Q: dz Given z = xy + sin(xy2), with x(t) = 2t + 1 and y(t) = -t², find dt t=1

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Q: Determine the solution for the following higher-order nonhomogeneous differential equation. Also,…

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Q: In problems 3-5, use the building block n=0 Σ", <1, together with the result differentiating and…

A: Note : As per our guidelines , we can solve first question . Please repost remaining question .

Q: Consider the following. 300 (1.025) 5 = 1100 (a) Find the exact solution of the exponential equation…

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Q: Problem 2. f = Is the integral XT dx convergent or divergent? Hint: There is a test that allows you…

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Q: If ƒ(x) = (x² + 4x + 5)², then f'(x) = 4x³ + 24x² +52x + 40 f'(2) =

A: Given f(x)=(x²+4x+5)²

Q: Let z = 6ex²y³. Then: дz дх дz ду

A: We can solve this as follows:

Q: 3 2x S 2 (1-x)² -dx

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Q: The linear approximation at where A is: and where B is: = 0 to sin (3x) is A + Bx

A: We need to find Linear approximation.

Q: 21-22 Find y' and y". 21. y = x² ln(2x)

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