A balloon which maintains the shape of a sphere is being inflated. The rate of change of its volume £t° /ft. with respect to the diameter at the instant when the diameter is 2 ft is 2T 8T O 4T 16m

Q: Find f'(a) using the definition of the derivative at a point for: f(x). 1 = √x at a = 4.

A: Find derivative using  definition of f(x)=1x at a=4

Q: Given z = 7t - 43 and y = 49 sin t dy (i) de to (ii) (1₂)

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Q: c - [ ²x² (1-√x ) ³dx Jo

A: To find out the integration.

Q: For the function f(x)=x^3-3x+1 defined on the interval -3 ≤x≤3. Find absolute maximum and minimum…

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Q: Solve the differential equation. 14. ( 1 – xy)^-2 dx + [y^2 + x^2 (1 – xy)^-2] dy = 0

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Q: Find the general solution for the following Second Order Deferential Equation: d²y Q4: dx² - y = ex…

A: The given differential equation is;  d2y/dx2 -y=ex+x2.

Q: да Given zTan¯¹ (x + y) — ln [1 + (x + y)²] = 5%, what is ду -1 2-2x-2y none of the choices 2- 2x +…

A: ∂∂xtan-1x=11+x2 Note : As per our Guidelines , we can solve first question. Please repost remaining…

Q: (y^3 - x^3) dy = (3y•(x^2) +1) dx Solve exact diff eq

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Q: Suppose two positive real numbers a and b add to 120. Find the values of a and b that maximize the…

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Q: sec5 (sin ¹(7x)) √1 - 49x² dx

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Q: Use the binomial series to find the Maclaurin series for the function. 1 f(x) = (1 + x)4 f(x) = Σ n…

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Q: A=  0 0.3 0.25 0.1     D=  3 4

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Q: Create a question (using the Triangluar pyramid) related to vectors and then solve it. Don't make…

A: First we will frame a question and then solve it.

Q: Find the partial derivative of z with respect to x z = (3x² + 1) cos(x²y). əz = -2x (3x² + 1)…

A: Given function z=(3x2+1)cos(x2y)

Q: Ismael made an error when he was evaluating log3 27 - log3 9. Ismael's work log3 27 - log3 9 log, 27…

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Q: Find the slope for f(x,y) = xeyat P (2,0) in the direction of the line from M(2,0) to N(-1,2)

A: We have to find slope

Q: Let f denote the function if x < 2; 1 f(x) = if x 2. Which of the following is true about f? Of is…

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Q: Find the general solution of the given ODE * dy x+2y-3 dx 2x+y−3 (x+y)³ = C(x + y − 2) Option 1…

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Q: 3. find the derivative 513.5+412.52¹.7 lt Enter your answer

A: Taking derivative of the function with respect to t and using power rule of derivative gives the…

Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

A: Solve the following

Q: 2. f(x) = 1 x²-1

A: We have f(x) =1x2-1

Q: Using the graph of g(x) below, answer the following questions. a) Where is g′(x) > 0?     b) Where…

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Q: Suppose that a product currently sells for $24, with the price increasing at the rate of $5 per…

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Q: 4. Find the volume generated by revolving the area cut off from the parabola y = 4x - x² by the x…

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Q: find  the area of the  region bounded by the  curves y²=4px and x²=4py

A: To find the area.

Q: d- d³y dx3 d²y +6 dx² - Q.2-Solve the differential equation 15 - 100y = 0 dy dx

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Q: 4) x(xdy - yox) = y² lnx dx

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Q: In sketching y= O None of the choices O y = 1 O x = 1 O No horizontal asymptote (x-1) In z determine…

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Q: x≤2 Q3. Find the value of k so that f(x)=(x², k-x², x>2 is continuous at x = 2

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Q: A small hole on the sack of rice cause some rice to be wasted while the sack is being lifted…

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Q: Graph the parabola. y=x+2x-2 Plot five points on the parabola: the vertex, two points to the left of…

A: We have to find the graph

Q: Graph the function. f(x)=3√x-5 Plot four points on the graph of the function: the leftmost point and…

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Q: 2. f(x) = 4x5 + 3x² - 7

A: To discuss the continuity of the given function. To give the intervals in which he function is…

Q: Suppose a person is going up in a hot air balloon. The surrounding air temperature in degrees…

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Q: 50 own. Draw the graph of y=g(2x).

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Q: wing is Of has a relative minima at x = -3 and x = 3. OIt cannot be determined if has any relative…

A: To find the relative maximum and minimum of the function

Q: 6. cos x sinỗ xdx

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Q: A conical vessel is 12 m across the top and 15 m deep. If it contains water to a depth of 10 m, find…

A: We need to consider a section and then integrate accordingly.

Q: A ball is launched straight up in the air from a height of 5 feet. Its velocity (feet/second) t…

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Q: An economy depends on two basic​ products, wheat and oil. To produce 1 metric ton of wheat requires…

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Q: An ice cube is freezing in such a way that the side length s, in inches, is s(t)=t+6, where tis in…

A: Write down the equation of the volume.

Q: The difference between the number of arrangements using all the letters in DIPLOMA and the number of…

A: We need to find difference between arrangements.

Q: I Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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Q: 1. S (x¹+3x²+1) dx 2. f(x³ + x² + x−¹)dx p³ +p²+p+1 dp 3. p3 √ 2² (√z + √z-1) dz 8x³+27 -dx 2x+3 5.…

A: The objective of the question is evaluate the anti-derivative.

Q: c) f(x)=tan(cos².x) 11 COS X 1+ sin.x Dy=- b) y = 2

A: e)  f(x)=tan(cos2x)  f) y=cosx/(1+sinx) g) y=ex^2/x3 Repost the next part.

Q: d- ax d² y +6. dx² d³ y dx3 - - Q.2-Solve the differential equation dy 15 - 100y = 0 dx

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Q: -21 Give a general solution of the differential equation y"-2y'-8y = 3te ²¹.

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Q: √x²-3-1 x - 2 A. lim x-2 tet B. lim to et +1 C. lim x→1 x² + x - 2 x² - 1

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Q: (X^1/2 + 6) (X^3/2 -32)

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Q: On which of the following intervals is the function f(x) = x3 differentiable? (0, +∞0) 0 (-00, +∞0)…

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