Evaluate 3+x lim,→4 (c-4)(x+2) O +∞ O 1 8.

Q: Calculate the area enclosed by the f(x) = x3 – 6x² + 8x and the x-axis. curve

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Q: Find V· (F x G), if F(x, y, z) = 10xi +j+7yk and G(x, y, z) = xi+ yj – zk. V · (F × G) =

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Q: Solve the system of equations using matrices (row operations). 3z- 3w = - 4 X+ y+ z+ 3w= -1 2x + y-…

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Q: The region bounded by the given curves is rotated about the specified axis. Find the volume of the…

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Q: Using the laplace transformation formula, ∫ f(t) e^−st dt evaluate L[15-3t]

A: The given laplace transform,  L15-3t

Q: Describe the graph of the equation. r = 10 cos ti + 8 sin tj – k O It is an ellipse in the z = – 1…

A: Given that       r = 10 cost i + 8 sint j - k

Q: Solve following diffrential equation x(dy/dx)+6y=9x^2

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Q: Consider a wood beam (see figure) carrying a uniform load of 20.5 kN/m (which includes the weight of…

A: answer is in next step

Q: ||r(t) × r"(t)|| ||r(t)||° Use the formula k(t) to find k(t). r(t) = t'i + tốj K(t) =

A: We can solve as follows

Q: Vx² +y² and A metal plug has been designed using the intersection of the two cones z = x² + y2 += 1.…

A: We have to calculate volume of plug which is intersection of two cones z=√(x2+y2) and z/3+√(x2+y2)=1…

Q: If f(x) = V4x + 1 find f"(2). O 4/27 O 213 None of these O 2/3

A: Topic:- Derivatives

Q: You remove your pecan pie from the oven and place it on the counter for an hour before serving it.…

A: The temperature T in degrees Fahrenheit of pecan pie is modeled by T=f(t) where t is the time in…

Q: 4. Evaluate lim (cos r)/". エ→0

A: we want to find the limit limx→0 ( cosx )1x2

Q: Given f(x) = 3x2 – 24x + 15, a. Write f(x) in standard form. b. What is the axis of symmetry of…

A: Given query is to write the standard form and find symmetry.

Q: 3. If dt , find g'(2). 5. g(x) =

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Q: Find the center and radius of the sphere that has (7, –6, 2) and (9, 12, –6) as endpoints of a…

A: The objective of the question is evaluate the center and radius of the circle

Q: 2) Center: (11, 16) Radius: 1 4) Center: (-4, 0) Radius: 7 6) Center: (-7, -12) Radius: 3 8) Center:…

A: The Equation of a circle : (x - h)2 + (y - k)2 = r2 Where, r = Radius of the circle (h,k) = Center…

Q: (i) Using Laplace's equation, find v,and və for inviscid vortex flow.

A: answer is in next step

Q: 6/9 Correct Question 8 of 9, Step 1 of 1 Find the total area bounded by the x-axis and the curve y =…

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Q: Evaluate the integral / (2x + 9y)dx + (6x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

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Q: —2х Se-2x sin 3x dx

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Q: Evaluate the integral (8x + 12y)dx + (9x – y)dy along the parabolic (8x +12y)dx + (9x – y)dy along…

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Q: Find div F and curl F if F(x, y, z) = xz°i+ 2y°x²j+2z²yk. %3D div F= curl F=

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Q: Double USA, manufacture of the Nicolas cage pillow has determined that the marginal daily revenue…

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Q: Find the area with respect to y of the region bounded by x = y² + 2 , x = 0 , y =– 1, and y = 2. |

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Q: 1+ cx, if x 2 Given the function: f(x) = C - x, What should be the value of c so thatf is…

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Q: •5 f(x)dx = 6 and | g(x)dx= 2 , evaluate |3|

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Q: Consider the function y-2+3x² -x³ a) Find the intervals on which this Punction is increasing or…

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Q: Given the function g(x) 6x + 63x² + 216x, find the first derivative, g'(x). = (x),6 Notice that…

A: We use second derivative test to determine the local Maxima and minima

Q: sin? (x) cos (x) dx

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Q: A ball is thrown into the air and its position is given by h(t) = - t² + 85t + 2 where h is the…

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Q: Find V. (V x F), if F(x, y, z) = 6e"²i+ 2xe³j – 3ek. - V·(V × F) =

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Q: Evaluate the line integral (2x + 4y)dx + (3x – 9y)dy along the curve C : æ = 2 cos t, y = 4 sin t (0…

A: We need to evaluate integral.

Q: 4- part 1 Find the derivative of the function f(u) = 4u° 4 - 2u1.8 0.4 %3D = (n),1

A: Differentiate wrt u

Q: Find the area of the region bounded by the graphs of f(r) =-r² + 2x+5 and g(z) = 121|- %3D

A: Area bounded by the curves :  If f(x) and g(x) are two continuous function on a,b and f(x)≥g(x) on…

Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

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Q: Find the derivative of f(x) = (2 - 3x) (-5x + 4). O 2 О 22-30х О зох + 22 30x + O 15x + 8 None of…

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Q: Use Stokes' Theorem to evaluate curl F. ds. F(x, y, z) = ze'i + x cos(y)j + xz sin(y)k, S is the…

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Q: Evaluate lim, (-5x + 5 – 5 - ) 12 O + O 5 O-5

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Q: Qu= O.4 log (E+0.44 435 %3D Qa - 0.249(log Ea)-O.I77 Q8= 0.227 (log E3)-0.839 Q3= rearange equations…

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Q: Find the derivative of the following equation: (2x – 1) (3a? + 2) - O 48x + 36x2 + 22x + 8 48x3…

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Q: A rectangle sign has a perimeter of 72 ft and an area of 320 ft2. What is the length and width of…

A: Solve the following

Q: 3. Suppose that the revenue in selling a tables is equal to 200x-0.25a2 dollars, and producing a…

A: topic - application of derivatives

Q: S 289 xe

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Q: 22 r = 7 sin 0 + 50 cos O

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Q: Test the convergence of cach of the following two scrics. n" 2n +3 (1) 2 n! (ii) Зп + 2 n=1 n=1

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Q: Find T(t) and N(t) at the given point. r(t) = 11 cos(t)i + 11 sin(t)j + tk; t= -11 /122 T(5) V122 0,…

A: Given: r(t)=11cos(t)i→+11sin(t)j→+tk→ r'(t)=d11cos(t)dti→+d11sin(t)dtj→+dtdtk→…

Q: manager sells 75 cakes per week at 650 pesos each and he knows that for every 10 pesos crease in the…

A: Given query is to find the price tk maximize the revenue.

Q: Sheldon is being chased back-and-forth by a dog along Euclid Avenue. His directed distance (in…

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Q: Evaluate the integral (8x + 12y)dx + (9x – y)dy along the parabolic (8x +12y)dx + (9x – y)dy along…

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