Draw and label diagram to help solve the related-rates problem. The radius of a sphere decreases at a rate of 3 m/sec. Find the rate at which the surface area decreases when the radius is 10 m. ⒸRice University 20

Q: Find the derivative of the function. g(x) = 6x ² - 1 [Sx U 4x u²+1 du

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Q: Use the linear approximation of f(x, y) = e²x²+2y at (0, 0)

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Q: A projectile is launched into the air. The function h(t) = -16 + 32t + 128 gives the height, h, in…

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Q: Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 9…

A: Topic = Area

Q: Find the derivative of y with respect to x; where x = 2 tanht & y = 4 sech t when t = 0.

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Q: At what point (x, y) is the function f(x) = 2 - 4x closest to the origin? Enter an exact answer.…

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Q: Find the gradient of the function f(x, y, z) = zy², at the point (0,-1,-1) ▼ƒ(0, −1, −1) =

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = √√1+3x,…

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Q: Estimate f(-1.02, -0.97) given that f(−1, −1) = 3, fx(−1, -1) = −2 and fy(-1, -1) = −1.

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Q: Find the 10th derivative of the function: y = (x+1)/(x-1)

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Q: The side of a cube is measured to be 21 cm, with a possible error of cm. A. Use differentials to…

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Q: A company manufactures and sells x cellphones per week. The weekly price-deman and cost equations…

A: NOTE: Refresh your page if you can't see any equations. . the given demand function is and the cost…

Q: Find the absolute maximum and absolute minimum of the function x3 3 f(x) = 1 7x² 2 + 10x - 2 over…

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Q: 22 Use the method of variation of Solu Parameters to find the particular solution of the following…

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Q: Study the asymptotic behaviour for n→ +∞ of the sequence 1. an = 1-n² n+3

A: 1. According to the question,Given sequencean = 1-n2n+3

Q: Let ƒ(x) = x³ – 15x² +27x - 2. Find the open intervals on which f is increasing (decreasing). Then…

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Q: A juice company has found that the marginal cost of producing x pints of fresh-squeezed orange juice…

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Q: Find the minimum and maximum values of the function f(x, y) = x2y4 subject to the constraint x2 - y²…

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Q: z = sin(x² + y²), x = v cos(u), y = vsin (u), find az/au and az/av. The variables are restricted to…

A: We have to find the derivative using chain rule.

Q: Calculate the sum of the series Sn = 2-6(0.9) 00 Σan whose partial sums are given. n = 1

A: NOTE: Refresh your page if you can't see any equations. . for the series the partial sum is  .

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y=x²-In(x),…

A: y=x2/4 - ln(x)/2

Q: 2) Evaluate 21 xy SS₁ XV y dy dx 1 +

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Q: Find the slope of the following lines.

A: see below the answer and calculation

Q: A curve with polar equation 31 7 sin +36 cos 0 represents a line. This line has a Cartesian equation…

A: NOTE: Refresh your page if you can't see any equations. . use the polar to cartesian substitution

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y=√√7-x, 1≤x≤7 X

A: The given curve is:y=7-x ;          1≤x≤7

Q: Determine whether the function's vertex is a maximum point or a minimum point and find the…

A: Given that: function is y=x-18x2

Q: 73. Which statement determines if set x is a proper subset of set lyl? 1. 2. 3. 4. x.issubset (y)…

A: If there are Two sets X and Y, such that X is a proper subset of Y, it means Y contains all the…

Q: The weight of a lake trout as a function of age satisfies the formula where Wis in kg and t is in…

A: The weight of a lake trout as a function of age satisfies the formula Wt=241-e-0.22t3 We have to…

Q: Use the limit process to find the area of the region between the graph of the function and the…

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Q: 3. Use cylindrical coordinates to evaluate 3 √9-x² [² [³²*² [√²²+³ (2² + y²) ³¹ dzdydz 0 Jo

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Q: Find lim (1+ I-X 4 T

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Q: At what point (x, y) is the function f(x) = 8x - 3 closest to the point (3, -6)? Enter an exact…

A: To determine the point x, y on the function fx=8x-3 is closest to the point 3, -6.

Q: 2x³ + 3x² √1+2x3 dx 2.S 2²/1

A: I = 2∫  2x^3 + 3x^21 + 2x^3dxI = 2∫  2x^3 1 + 2x^3dx + 2∫   3x^21 + 2x^3dxI = 43∫  x . 3x^21 +…

Q: couple received a $131,000 inheritance the year they turned 48 and invested it in a fund that earns…

A: According to the given data we have the following: present value of deferred annuity=$131,000…

Q: Use Newton's method to approximate the x-coordinate of the point where the graph of 4x3 - 10x-5…

A: NOTE: Refresh your page if you can't see any equations. . the given function is  and the given line…

Q: V₁² W V4 0 -21 V2 V3, and v4 are given below. -9 Then H and K are subspaces of R³ In fact, H and K…

A: we will find the required.

Q: The supply and demand for a product are given by 2p - q = 100 and pq = 300 + 25q, respectively. Find…

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Q: Use completing the square in order to put the followingation into te of the standard quadratic…

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Q: a. Find the linear approximation for the following function at the given point. b. Use part (a) to…

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Q: f(x) = x³ − 15x² +27x2. F

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Q: How much must be invested at the beginning of each year at 12%, compounded annually, to pay off a…

A: It is given that  We need to invest some money at the beginning of each year at 12%, compounded…

Q: Verify that the given vector field h is a gradient. Then calculate the line integral of h over the…

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Q: Find the absolute maximum and minimum values (show final answer as an exact value): f(x) = 2-sin r…

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Q: A supply function and a demand function are given. Supply: p=q² +8 Demand: p = 73 - 29- 29² (a)…

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Q: / x + 1 x² + 2x dx

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Q: The figure above shows the graph of the continuous function f. The regions A, B, C, D, and E have…

A: The area of region A =5It is above x - axis therefore, ∫-7-5f(t)dt = 5The area of region B =2That is…

Q: have found the minimum distance using the second derivative and write a thorough conclusion. to a…

A: Given:    Curve      y=lnx2   Let x,y be point on curve             Another point is 52,0 We know…

Q: 7 п 6 S y 4 3 2 4 ·10 Average rate of change = Number 6 Estimate the average rate of change from z =…

A: To find the average rate of change of function

Q: Evaluate the integral using the following values. 8 ["x² dx = 960, ["x ax = 24, ["ax=4 dx dx J4…

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Q: Find the particular solution to the differential equation. 2xy = y² +1 when x = 1, y = 2 dx

A: Given that        2xy(dy/dx) = y2+1    when x=1, y=2