etermine the instantaneous rate of change of the function πt √√x sin (772³) dt : x = 1. x3 1 + √t

Q: Let h(x) = f(g(x)) and p(x) = g(f(x)). Use the table below to comput derivatives. a. h'(2) b. p'(1)…

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Q: Given Cost and Price (demand) functions C(q) = 110q+45000 and p(q) = -2.7q+800, what profit can be…

A: Given cost and price (demand ) function C(q) = 110q+45000 and P(q)= -2.7q+800q, what profit can be…

Q: dy √y+4-2 5. S

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Q: quickly

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Q: (a) a) ₁₁ (x² +y) dy dx. Show all your work! 2 (b) ***1 1 dy dx. Show all your work! 0 2 ¹y² ff 1 dx…

A: SOLUTION-

Q: Find the directional derivative of the function f(x, y) = √√√x + 2y at the point (2, 1) in the…

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Q: of convergence of too0 n 3"x" na n Find the interval the power series

A: Given problem:-

Q: Find the linear approximation of the function g(x) = 1 + x at a = 0. g(x) * Use it to approximate…

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Q: The Bradford family wants to establish an ongoing scholarship award at a college. Each year in June…

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Q: 8. Find the area of the region in the first quadrant bounded by the curves y = sin x, y = cos x and…

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Q: Suppose that $2,500 is deposited into an account paying 6.2% interest compounded continuously.…

A: $2,500 is deposited into an account paying 6.2% interest compounded continuously.

Q: 1. An open box is to be made from a 20-inch by 32-inch piece of cardboard by cutting out x-inch by…

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Q: If F(x) a. F'(1) L √4t - t² dt, evaluate the following: x² b. F(2), by interpreting F(2) as an area

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Q: 1 вхось xа(1 — x)bdx - = 6xº1 Bx®1 - x)dx /0

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Q: 00 ermine the converges or diverges of the series n=1 = 1 (n+1

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Q: Determine whether the series k=1 3\k-1 converges and if so, find its sum.

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Q: Find the dimensions of a rectangle with area 1,728 m² whose perimeter is as small as possib m…

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Q: 2. Using power series, evaluate lim x → 0 sin x-x 3 X

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Q: too (-1)³²x²² 4) Let sinx= -1=0 2ntl a) Find a power series for xsinx b) Differentiate the power…

A: Here is the solution:

Q: Determine whether the improper integral converges or diverges, and find the value if it converges.…

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Q: Given: cos 3y + sin 2x 2 cos 2x 2 O -3 sin 3y-3 -2 cos 22-2 O -3 sin 3y 3 O -2 cos 2x-2 3 sin 3y 3 2…

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Q: Show that the substitution a = e, y = et converts the equation ди ² (0²²) + 1² (0²5²) +- (3) +v(u) =…

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Q: The height of a projectile launched into the air is given by f(t)= - 16t² + 220t + 10, where t is…

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Q: For the function f(x,y) = √y² + 5x², find f(2, - 5), f(− 1,2), f( – 3, – 5), and f(0,9). f(2,-5)=…

A: Given query is to find the value of the function at indicated points

Q: A bacteria culture initially contains 1000 bacteria and is growing at the rate of N' (t) = 2tt-2/3…

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Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: The equation of the curves are: C1: y = x2 ⇒ x = y                 for first quadrantC2: x = y2 To…

Q: The amount of a certain substance in a chemical compound is given by the function C (t) = 20.6…

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Q: If (2, 1) is a critical point of f and fzz(2,1)ƒyy(2, 1) < [ƒzy(2, 1)]², then ƒ has a saddle point…

A: Here, the given statement is: If (2,1) is a critical point of f and fxx(2,1)fyy(2,1)&lt;fxy(2,1)2…

Q: Find the area under the curve 4x2-3x+6 between x= -2 and x=3

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Q: Find fx (x,y) and fy(x,y). Then, find fx(-1,-4) and fy (-3,2). 32 f(x,y) = 4x³y² fx(x,y) =

A: We have to find partial derivatives of Given function.

Q: A cylindrical can without a lid is to be constructed to contain 800 ml of liquid. Determine the…

A: To find the dimensions that minimize the amount of metal needed to make the can.

Q: Given cost and price (demand) functions C(q) = 110q+41,500 and p(q) = -1.9q+870, what is the…

A: Given  Cost function C(q) = 110q + 41,500  price function p(q) = -1.9q +870

Q: Newton's law of cooling states that the temperature of an object changes at a rate proportional to…

A: We need to find D.E&gt;

Q: 2. lim (x - Inx)* x)² 2-0+

A: Here, the given limit is: limx→0+(x-ln x)x which is (-∞)0 form.

Q: The height of the ball when its velocity is 0 ft/sec. is feet.

A: First, we will find the velocity of the ball at t second. Then we will find the value of t for which…

Q: A car is slowing down at the rate 0.8 ft/sec². How far will the car move before it stops if its…

A:

Q: find the symmetric equation of the line through point (1,-2,-4) which is orthogonal to the plane…

A: We have to find the symmetric equation of the line through point (1,-2,-4) which is orthogonal to…

Q: 22. =2x²-3x+1 at (-1, 6)

A: Topic = Derivative As per guidelines , At a time only one question can be answered. please repost…

Q: Partial Sums An arithmetic sequence has a first term of -1 and a common difference of -17. If S₁,…

A: We have to find the sum

Q: Convert each degree measure to radian measure as a multiple of . Do not use a calculator. (a) 135°…

A: We know that for converting degree to radian , we multiply by factor π180° Therefore

Q: 2x x→∞ 3x² +5 3x xx√√√x² x² +4 X lim x→→∞ 2 sin î (a) lim (b) lim (c)

A: Given

Q: Perform the integration. (sinh x)(coth x +csch3x) dx +

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Q: 4. If a 32 foot chain is hanging (balanced) on a metal peg on a wall. At time t=0, with the chain…

A: Given that,

Q: Sketch and set up integrals for volume of the region bounded by y = x^2 + x - 2 and y = 3x + 13…

A: Please see the below pictures for detailed solution.

Q: Help

A: Please refer to the image below

Q: Suppose the labor cost (in dollars) for manufacturing a camera can be approximated by 3 L(x,y) = x²…

A: We will use partial derivative to find x and y.

Q: 120 5+sin 0 5. (a) Find the constants a,b,c for the conic r=- Sketch the conic.

A: Concept: The standard form of the polar cone r=a(1-e2)1±esinθ Here e is the eccentricity When the…

Q: Given Cost and Revenue functions C(q) =q³-9q² +53q + 5000 and R(q) = -3q² + 2500q, what is the…

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Q: Using the shell method, what will be the equation of the volume of the solid formed when the region…

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Q: What is the y-coordinate of the centroid of the plane region bounded by y = x^3 and y=x^2? O 2/5 3/5…

A: We can solve this as follows: