Use the formula ‹(t) k(t): = ||r'(t) × r"(t)|| ||r' (t)||³ = r(t) = e³ti + e-tj to find (t).

Q: 8. Use differential to estimate the value of √ 4.01 four decimal places. 9. Use differentials to…

A: We have to find 8.The value of √4.01-1/√4.01 upto four           decimal places.  9. The value of…

Q: Solve for the derivative of the following trigonometric functions. 1. f(x) = e3x 2. f(x) = x³ ex 3.…

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Q: Verify Green's Theorem by evaluating both integrals ON √ y² dx + x² ov - [/(2x - 2M) da dA R ax ду…

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Q: of a rectangle.

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Q: A curve with polar equation represents a line. This line has a Cartesian equation of the form y = mx…

A: To write the given equation in the form of y  = mx + b.

Q: (D² − 4)y = 8e²x – 12 -

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Q: Match the vector field with its graph. F(x, y) = yi 1 |||||||||| 三 6 靈

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Q: 5x²³-4x²+3x LX Find the most general antiderivative of the function: f(x)=-

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Q: Solve the D.E ý - 25 +2y = 2X+3

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Q: ☎ Q1: If x=² and y=21³ then b) 3 314 ² dx d) at x=4 F others Choose

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Q: Find the area of the region enclosed by the parametric equation x = t³ - 7t y = 6t²

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Q: = fºx R/2 Given that evaluate - b² = g², use this result and the fact that 2 (6 cos(x) - 6x) dx. x…

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Q: Find an equation for the conic that satisfies the given conditions. parabola, focus (5, -3), vertex…

A: The general form of the parabola is given by: y=a(x-h)2+k...(1) where (h,k( is the vertex of the…

Q: Find the limit. lim 1→2(t i - 5 j + t² k)

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Q: Find the derivative of the function. h(t) = - (²²) ² h'(t) =

A: We have to find derivative

Q: Replace the Cartesian equation with an equivalent polar equation. x² + y² = 100 Or-10 sin 0 Or- 10…

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Q: If a cup of coffee has temperature 95°C in a room where the temperature is 20°C, then, according to…

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Q: interval of convergence = 0

A: Follow the procedure given below.

Q: Find the Maclaurin series centered at c and the interval of convergence. 12) f(x) = 1-2x 13)f(x) =…

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Q: Suppose that f(x) and g(x) are given by the power series f(x) = 3 + 4x + 3x² + 2x³+... and g(x) = 6…

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Q: Suppose that the revenue in selling x tables is equal to 200x – 0.25x“ dollars, and the cost of…

A: Here is the solution:

Q: 8. The position function of an object is defined as: s(t)= t³-t²- 8t Find the minimum velocity of…

A: As per our guidelines we are supposed to answer only one. Kindly repost others question as a…

Q: Find the one-sided limit (if it exists). (If the limit does not exist, enter DNE.) 2√x lim CSC X

A: Explained below

Q: Find the tangent line approximation T to the graph of f at the given point. Then complete the table.…

A: To find out the tangent line approximation.

Q: Prove the identity. sin 2, x = 1- cos x 1 + cos x Note that each Statement must be based on a Rule…

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Q: ergence or divergence of the given series or state that the Root Test is in 1 n=1 non x.)

A: Given :

Q: Solve the following differential equations of d² y dx² dx dy +3 dv −10y=3x²

A: We have to find the solution of the given differential equation.

Q: Find all solutions to the equation. csc 0-√2=0 Write your answer in radians in terms of , and use…

A: As we know that; The general solution of the trigonometric equation sinθ=sinα is; θ=kπ+-1kα,  where…

Q: Find the volume of the solid generated when the region enclosed by the given curves is revolved…

A: This question is based on application of integration.

Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

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Q: Monique sells disposable protective face masks made of local textiles for P 12.00 each. Define a…

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Q: Use the ratio test to find the radius of convergence of the power series R = (If the radius is…

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Q: 2. Find the area between the curve y=-x and y+x²= 2x.

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Q: Find the integral of the following equation integrate (cos x)/(1 - cos^2 x) dx

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Q: Use the Root Test to determine the convergence or divergence of the given series or state that the…

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Q: 6. 2x³ cot x4 dx 7. S x4 sec (x5 - 9) dx 8. Stan ³ x dx

A: We can solve this as follows:

Q: Suppose you deposit $1000 at 7% interest compounded continuously. Find the average value of your…

A: To find out the average value of account during first 4 years.

Q: Let f(x) be a function and let c E R. Which of the following is not represented by the derivative…

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Q: For F(x, y, z) = (x + yz) i + (y + xz)j + (z + xy) k, find: (a) the curl (b) the divergence

A: To find curl F and div F

Q: h₂ = = 3.75 sin(736t) + 7.5 and h₂ = 3.75 sin(736(t + 4))+ +7.5

A: answer of given question is in next step

Q: Solve the following initial value problem: y′′+6y′+18y=0y″+6y′+18y=0 when y(0) is 5 and y’(0) is…

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Q: Find the exact length. T=0², 0≤0 ≤ 2π ° 4[G²+1²] ²3 [(x² + 1)² - 1] [(²+1)-1] ° 4[68² +1²]

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Q: Calculate the length of the path over the given interval. (sin 7t, cos 7t), 0≤t≤n

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Q: SKETCHPAD Write the formula to represent the nth term of the following sequence. 6, 17, 34, 57, 86,…

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Q: enclosed by the Curve Find the area X = 2y² and x = 8

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Q: Given: (x is number of items) 3844 Demand function: d(x) = √x Supply function: s(x) = 4√x Find the…

A: The demand function is given by dx = 3844x The supply function is given by sx = 4x To evaluate: The…

Q: Find the area between the loops of the limacon r = Area = 5(1 + 2 cos 0).

A: We have to find the area between the loops.

Q: = The Taylor series for f(x) = √2x − x² at a : 1 is Σ Cn (x - 1)”. n=0 Find the first few…

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Q: Find the nth Taylor polynomial centered at c. f(x) = ln(x), n = 4, c = 6 P4(x) = X

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Q: Find the exact length of the curve. X √(y - 3), 16 ≤ y ≤ 25

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