For the function f(x) = 42² +5z, evaluate and simplify. f(x+h)-f(x) h ƒ(z) .

Q: When an object is removed from a furnace and placed in an environment with a constant temperature of…

A: The given problem is solved below in detail.

Q: In (x² + y² ) = 2 arctan y' 9 X

A: We know that derivative of xn is nxn-1.     Here i attached the solution of this question.

Q: The base of a the y-axis are triangles with the height equal to 2. Algebraically, find the area of…

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Q: Evaluate the iterated integral. (x + y²) dx dy THERE

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Q: Determine if y=5 cos x and x=31²-5t+3 dx

A: Given,             y=5cosx , x=3t2-5t+3To find : Determine dydt

Q: √81 - y² ST (x + y) dx dy

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Q: An experienced carpenter can frame a house twice as fast as an apprentice. Working together, it…

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Q: 1. Use the graph of y = f(x) given below to find the answer to each of the following. You do not…

A: By using the graph of y=fx given below to lisy all the intervals on which f is increasing.

Q: 2. Find a power series solution of the differential equation y' = 4y

A: To find a power series solution of the following differential equation.y'=4y

Q: 8. eeer +eyty dy

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Q: Evaluate the iterated integral. [²] (x² - y²) dy dx

A: Given: I=∫-11∫-44x2-y2dydx   As we know that; The Power rule; ∫xndx=xn+1n+1+C

Q: Question 3 Differentiate: y = arccot (x)+ arctan 01 O (E) None of these Ⓒ2x O 1-2x O < Previous 1-2z

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Q: 3. Find of the following equations: dx a. y = (e-3x² + 7x² + In 8x)* b. √xy = 2x²y - 8x c. x = sec…

A: Just taking derivative of problem (b) and using product and chain rule of derivative and then…

Q: 6. Using a double integral, find the area that is inside the region bounded by r = 3+2 sin and r =…

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Q: Question 8 Find the derivative -[f (x)] dx Anmospace support = 3 In (In (x²-3x + 5)²) 3(2x - 3)…

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Q: Consider the function f(x) = cos(x) - Give the following: A = B = f" (A) = f" (B) = Thus f(x) has a…

A: The given function is  f(x)=cos(x)-sqrt(3)x/2.

Q: Evaluate the iterated integral. [[ (x + y) dx dy

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Q: Set up integrals for both orders of integration. Use the more convenient order to evaluate the…

A: Here, ∫R∫yx2+y2dA is evaluated where R: trapezoid bounded by y=x, y=8x, x=1, x=8 which is:

Q: 1. Given the following matrices: 12 3 41 4 2 4 6 8 A = B = 85 1 3 5 7 4 4 2 a. [(AC)BT] - DT…

A: Given the following matrices:A=123424681357-12-34, B=479853442, C=112335-23-4-1-11,…

Q: Convert the following lines to parametric equation. a) l₁: = (1,0,1) + t(1,0,−2), t = R Z-3 b) 1₂: x…

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Q: x²-3x - 7 2 (x² + x + 2)(2x - 1) dx

A: Simplifying the given integrand: x2-3x-7(x2+x+2)(2x-1)=x2-3x-72(x2+x+2)x-12

Q: Is partial fraction decomposition always possible? If YES, Explain If NO, Explain

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Q: The table shows a proportional relationship between the number of tickets purchase and the cost.…

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Q: Find T(t) and N(t) at the given point. r(t) = (t²- 2)i + tj; t = 2 T(2) N(2) = =

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Q: Use implicit differentiation to find the equation of the line which is tangent to the curve 2xy +…

A: Given equation: 2xy+3x2-5x=4 We know that slope of tangent will be defined by dydx-1,2

Q: Find a, and d for each arithmetic series. 61. $20=1090, 420= 102 63. S16-160, a16-25

A: Given that : S 16 = -160 and a16 . = -25.  is for a arithmetic series.   And we find the value of a1…

Q: Suppose f(x) = x² - 4x-9. Compute the following: A.) f(-3) + f(2) = B.) f(-3)-f(2)= =

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Q: 2. y = x² sinx What is the appropriate formula? dy Solution:

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Q: du (u² + a²)² √

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Q: 4. Use cylindrical coordinates to evaluate [!] √²³² + y²dv₁ D where D is the region that lies inside…

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Q: Consider sin¹x cos³x dx. If we let u= sinx, the integrand can be transformed to

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Q: find the equation of the line that passes through the point (-1,3) and is parallel to the line…

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Q: Question 1 Differentiate: arcsin Oy/x 01 O x/y O (E) None of these 0 0 (# )+ + arccos (²-) = 1

A: Differentiation

Q: Find sets of parametric equations and symmetric equations of the line that passes through the two…

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Q: Find Lt+1)²-e' sin² t + cos(t+1 ++ π)}.

A: Given :

Q: d Calculate [ri(t) r2(t)] and Calculate[ri(t) r₂(t)] and [ri(t) × r₂(t)] first by differentiating…

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Q: Determine whether the improper integral diverges or converges. 00 x²ex dx 0 O converges O diverges…

A: Given query is to find integral converges or diverges.

Q: The equation of motion is given for a particle, where s is in meters and is in seconds Find the…

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Q: 25 2 la

A: We have to find the following conditions according to the given information

Q: 5. What is the derivative of the given function below? * x² + y² = xy dy dy dx dx Option, dy dx = =…

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Q: Use any method to find the Area of domain bounded by curve parametrized by X = cos³t₁ Y = sin³t, 0≤…

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Q: 4. Compute each of the following definite or indefinite integrals. Show all work toward your answer.…

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Q: C. ¡(4eª + x¹/³)dx

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Q: So whats the answer

A: The question asked for the function f or ft. The last line was the answer.

Q: The radius of the base of a cone is 6 inches. The slant height of the cone is 10 inches. Which is…

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Q: Evaluate the iterated integral. LP'&x+yaxay (x + y²) dx dy

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Q: Find the limit. lim (t i − 3 j + t² k) 1-5 lim (t i − 3 j + t² k) − i 1-5 i k = i+ i j+

A: We can find the exact answer as below

Q: 5. Use spherical coordinates to evaluate [[[ (x² + y² + 2²) ² dv D where D is the solid hemisphere…

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Q: Find the derivative of f(x) = tan(sin(2x))

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Q: Write an equation of the form y=a sin bx or y=a cos bx to describe the graph below. y 0 4 5 16 7 8 9…

A: Given