2. Given the function: f(x) 3 x -3 x≤2 2 x² + 1 x > 2 Is f(x) continuous and differentiable at x=2?

Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = xy + yz + zx,…

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Q: If a force of 5lb produces a stretch of one-tenth the natural length L ft of a spring, how much work…

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Q: Approximate the area under the graph of f(x) and above the x-axis with rectangles, using the…

A: This is a problem related to area calculation using left hand points. Based on the reimann sum for…

Q: ) Find dw if w = xe³/², x = t², y = 1 — t, and z = dt 1 + 2t.

A: Topic:- application of derivatives

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Q: Compute the average rate of change of f(x) = x2 − 2x on the interval [1, 3]. Find c ∈ (1, 3) which…

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Q: Find the point of the porabola y=x²-4x+3 where the tangent is parallel to the line 3x+y=2. Determine…

A: topic- equation of tangent line parallel to given line

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Q: Use the Root Test to determine whether the series convergent or divergent. ∞ n² + 1 n 4n² + 5. n = 1…

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Q: Find the length of the curve y = ln sin x from t = −2 to t = 0.

A: f(x)=y=ln(sinx) Arc length =∫ab1+(f'(x))2dx f'(x)=dln(sinx)dx=1sinxdsinxdx=cosxsinx=cotx a=-2 b=0

Q: 2 Brad wants to buy a coffee machine for his café. The advertised price is $3200 including GST. When…

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Q: 7 =-=—=x² Find the center of mass of a thin plate of constant density & covering the region bounded…

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Q: Evaluate the definite integral. 5 4u [(-*--*--* du (u + 3)² 4 5 1 ((---)-D 4u du (u+3)²2 4 (Type an…

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Q: 6 cos3x cos4x dx

A: To evaluate: ∫π6π2 cos⁡3xcos⁡4xdx Let I = ∫π6π2 cos⁡3xcos⁡4xdx We know that 2cosAcosB =…

Q: 1. The figure shows the graph of a function f(x) with domain 0 ≤ x ≤ 3. Which of the following…

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Q: 6. If fand g are two differentiable functions at x, then 7. The derivative of the identity function…

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Q: Sx" xn sinx dx = −x” cosx+n n-1 cos x dx

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Q: (1 + x³) dy - x² y dx = 0, when x = 1, y = 2

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Q: 2 cos x = -0.7, 2TT ≤ x < 4T csc x = 2, 0 < x < 2TT sec x = -3, -π ≤ x < T 4

A: Given :cosx=-0.7cscx=2secx=-3

Q: Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a…

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Q: d. lim, In 1000 x ,5

A: Here, note that the function ln1000x grows asymptotically slower than the polynomial x5.

Q: ** Evaluate the following integral. Answer in 3 significant figure, exponential form, no units, no…

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Q: If y=u³ and u = 4x² - 2x + 5, give dy dx

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Q: S²₁ A Select one: dw w√w²+3 a. 0.0128 O b. -0.0234 0 с. c. -0.0128 O d. 0.0234

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Q: Find the inverse of the function on the given domain. f(x) = (x-5)^2, [5,00) f-1(x): =

A: The solution is given in the next step.

Q: A right circular cone has a constant height of 10 m. Find the rate of change of its volume with…

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Q: For each graph, choose the function that best describes it. (a) (b) (Choose one) (Choose one) (C)…

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Q: Find all the second-order partial derivatives of the following function. f(x,y) = x³y²-x² + y² 2 ax…

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Q: (1, -2) (a) The curve with equation y2 = x³ + 3x² is called the Tschirnhausen cubic. Find an…

A: We have to find the tangent equation and draw the graph.

Q: The graph of y=f(x) is shown. Draw the graph of y = -f(x). 17 Ex X 3

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

Q: 2 4 x + 8 d x (x+2) ³

A: This question is based on definite integral.

Q: In5 x ,2 limx→+00

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Q: Sx³√4 - 2x² dx 3

A: We have to solve integration

Q: Find Value of integral ) dx X+1

A: Given query is to find the value of the integral.

Q: The distance is (Type an exact answer, using radicals as needed.)

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Q: Evaluate the equation for f Select one: a. 0.5 b. -1 Oc. 2 Gd. 1 dzdy

A: Let I=∫01∫yy21y2-x2dxdyLetI=∫01(I2)dy                                    (1)WhereI2=∫yy21y2-x2dxWe…

Q: Assume that f(x) = 5x + 2 and f is defined on [-1,5). Then f has an absolute maximum value at 5.…

A: In given problem since function f (x) = 5x+2 is defined only on [-1,5) i.e. 5 is not in the domain…

Q: Let P be the point in 3-space with rectangular coordinates (√2, -√2, 2√3). (a) Cylindrical…

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Q: A forest has a population of lynx and a population of rabbits. Let x represent the number of lynx…

A: Let's solve given diffrential equation.

Q: Find the inverse of the coefficient matrix and use it to solve the system. = 6 2x₁ + x₂ X₁ X1 + 2x₂…

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Q: d. In 1000 x limx→+00 X5

A: Let's evaluate limit.

Q: 1) Find the radius of convergence and interval of convergence of the series. Show All Your Work.…

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Q: -1 √₂² (3+2u) du -2

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Q: √² (5x²-3x+18) dx 9x - x³

A: Integration is done by dividing polynomial.

Q: Topic: Area of Surface of Revolution The arc of the parabola y=x^2 from (1,1) to (2,4) is rotated…

A: We have to find the surface area.

Q: Evaluate the equation f f ² sin (ry)dyda Select one: O a. / O b. 2 c. O d. (²+4) (+4)

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Q: dx √x²-4x+13 S.

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Q: x==2t X 1 1-y = Given: line ₁ = -8 and ₂ = = y = 2+2t. 3 2 z = 6 + 2t 1. If the given lines…

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Q: Find the length of the are of the function x² = 4y from x = -3 to x = 3.

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Q: Find the derivative of the function y = (4x + 1)4(5x + 1)-5. dy (16x+4) 3 (4x+1)4 dx (5x+1)5…

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