Given R(t) = 4 costi + (1+ 3cost)j +5sintk. Find T(t). T(t) = -sin ti -sintj + costk Option 1 3 4 5 sin ti + sintj + costk T(t)= T(t) = -sin ti — sintj – costk Option 2

Q: Find the derivative of the function at På in the direction of u. x-y g(x,y) = xy+2¹ Po(1,-1),…

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Q: Find the derivative of the function using implicit differentiation.  1.) x²y + y²x = -2  2.) √(xy)…

A: 1.) x²y + y²x = -2    2.) √(xy) = x²y+1 ntiderivatives for integral notation. (x+7) dx

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Q: 5.) Find fog and go f, and their domains. f(x)=√x - 4, g(x) = x²

A: Given :f(x)=x-4g(x)=x2

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Q: e) Evaluate the following limit at infinity and show your work. 3x3-4x a) lim x→∞ x²-2x³

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Q: Evaluate the integral Sea X 6x³-1dx

A: This question can be solved using the concept of integration by substitution.

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A: Given:        Function gx,y=xy2   The gradient of function                  ∇gx,y=gx,gy   Taking…

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A: Evaluating the given integral

Q: • Evaluate the following integrals: Convert this Cartesian equation (x² + y²)²_9(x² - y²) = 0 to…

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Q: Evaluate lim f(x) using the graph of f. x→-4+ -6 10 2 6

A: This question is based on limits and continuity.

Q: 5-x Find the family of the curve whose slope at any point is y-3 passes through the point (2.1) and…

A: Topic:- calculus

Q: Find the linearization L(x,y) of the function at each point. f(x,y) = x² + y² + 1 a. (4,1) b. (2,4)…

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Q: (CLO-2) Find the linear approximation, L(x), to f(x) at x = xo - f(x)=√√6x+64, x = 0 O L(x)=-x-3…

A: Given f(x)=√(-6x+64)  We hav eto find the linear approximation of f(x) at x=0.

Q: f(x)=xe*, a =0

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Find the binommal coefficient (4)

A: Topic = Algebra

Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = 3 ex cos (yz),…

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Q: Evaluate the following integrals: O • (Cartesian to Polar) Civen the cartesian coordinate, find of…

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Q: Explain how you would graph the following set of parametric equations by plotting points and…

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Q: 10. Find the limit using any technique. The limit of f(x) = 2x² - 3 as x approaches -3. 15 21 limit…

A: To find limit of f(x)

Q: 2. f(x) = x³ senx cos x

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Q: 1) Determine the projection of a= [5, -4, 8] onto b = [3, 7, 6].

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Q: e²x-2x-1 x² f(x) = a) lim f(x) x⇒0+

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Q: 1 = and find x 1 Use linear approximation, i.e. the tangent line, to approximate as follows: Let…

A: This is a problem related to derivative of the function. Based on the general formula of linear…

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Q: 1. Evaluate the given integral Q. f(y-2x) dA, R where R is the region bounded by x = 0, y = x, x =…

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Q: x dv (2.v) - dx (V²1) dv (1+r) dx X 2 \-2 V-V²

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Q: x²-9 lim x-3 x-3

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Q: If the population of a city is 155,000. If the population declines continuously by 5% per year, what…

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Q: Find the approximate integral of 4 1 * -dx In x 2 when n=10 using a) the Trapezoidal Rule, b) the…

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Q: 3. A particle moving along the x-axis has velocity function v(t) = t²e-t. How far does the particle…

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Q: 5. Find the general equation of the circle of curvature of the parametric equation t+1 X=- 2 ; y =…

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Q: Find a formula bn for the n-th term of the following sequence. Assume the series begins at n = 1.…

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Q: The function f(x) = 2x³ +4.98x² + 26.2416x +2.34 is increasing on the open interval ( It is…

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Q: In this question, you will solve an integral problem using the method of substitution. (a) Make the…

A: A detailed solution is given below

Q: What is the exact area bounded by the curve f(x) = 1/2 X and the x-axis on the interval [1, 8]?…

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Q: The general solution of the D.E. dy/dx + y cotx = 1 is a. y -cotx + c sin x b. y = -tanx + C CSC X…

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: Which of the following statements about the graph of f(x) = (2.25) shown above are true? Select all…

A: Given graph of f(x)=(2.25)x

Q: The doubling time of an investment with continuous compound interest is 12.5 years. If the…

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Q: (CLO-1) Find the values of a and b such that the following function if x 1. X-1 D=

A: Topic:- application of calculus

Q: Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a…

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Q: 8. Evaluate z (9x² - (0x+6) dx

A: As we know that; The Sum Rule: ∫fx±gxdx=∫fxdx±∫gxdx The Power Rule: ∫xndx=xn+1n+1+C And…

Q: -1 √₂² (3+2u) du -2

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Q: Find the difference quotient x) = 2x² + 3x 2 - f(a+h)-f(a) h where h 0 of

A: Given query is to find the difference quotient.

Q: The population of a city is 323,000. The population declines by 3.8% every year, what will the…

A: topic- exponential function

Q: Problem #10] A kite 100 ft above the ground is being blown away from the person holding its string…

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Q: Use the shell Method to Find the Volume of the bounded by Solid generated by by revolving the region…

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Q: Using the fact that the centroid of a triangle lies at the intersection of the triangle's medians,…

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Q: Obtain the general solution unless otherwise instructed 2. y - y' - x = 0 Ус = Ур y =

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