Resources Let f(x, y) = In(x) + In(y), r(1) = (cos(t), t). Use the Chain Rule to calculate 4f (r(t)) at the value t = (Use symbolic notation and fractions where needed.) 1=x/4

Q: 1 for convergence, you can use the P-test. (You could also use the Integral Test, as To test the ser...

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Q: (-5t -2st1 Find the domain of f (t). Find the values of A and B if the function is continuous every

A: Here we have to find the domain of f(t) and the values of A and B.

Q: A cube is expanding at the rate of change 64 m³/s. What is the rate of change of its surface area wh...

A: This question is based on application of derivative.

Q: Activity 2.1 A. Choose the function whose derivative is equal to zero c. f(x) = 3x d. f(x) = V2r? a....

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Q: (a) lim e-" (x³ – x² + 9) sin x – x cos x (b) lim x→0 x – sin x (c) lim (x – In x)

A: We need to find limits. NOTE - As per Bartleby's guidelines we can solve only 3 subparts. Please upl...

Q: What is the linear approximation of the function f (x) = e x at x = 1?

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Q: Find an equation of the tangent to the curve given by y = t – In(t²) at the point corresponding to t...

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Q: this

A: We have to draw the graph of the following given function

Q: Deter mi.ne Particular Jolution y"-2y'+5y-0>y (1)=1,4'(7)•O

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Q: 8. k! k k=1

A: given series ∑k=1∞ k!k3

Q: Find the linear approximation for f(x)=sin2x at x=5π6 and use it to approximate sin2(147∘). Round yo...

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Q: Evaluate the following integral using partial fractions: 2x2 +1 dx J(x – 1)(x – 2)(x – 3) -

A: Given: I=∫2x2+1x-1x-2x-3dx   We know that; ∫1ax+bdx=1alnax+b+C And ∫a·fxdx=a·∫fxdx ; where a is cons...

Q: Test the series below for convergence using the Ratio Test. 87 n! n=1 The limit of the ratio test si...

A: Given query is to find series converges or diverges.

Q: y(x) =x' (2x – r²)

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Q: Solve the inequality. Write the solution set in interval notation. 6) 4w2 > 4w - 1

A: Consider the inequality  4w2>4w-1

Q: Verify that the two lines are parallel, and find the distance between the lines. (Round your answer ...

A: Given two lines, x=2-t, y=3+3t, z=4+3tAnd x=5t, y=1-15t, z=4-15tThat isx-2-1=y-33=z-43=t            ...

Q: Determine the convergence or divergence of the sequence with the given nth term. If the sequence con...

A: For the sequence convergence, limit n tends to infinity should be finite.

Q: Find the general solution to the differential equation: y' = 9° %3D

A: The given differential equation is: y'=9x   We know that; ∫axdx=axlna+C

Q: Use the root test to determine whether the series converges. If the test is inconclusive, then say s...

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Q: Let a = ci + j and b = 8i + 6j. Find c so that the angle between a and b is Round your answers to fo...

A: Topic = Vectors

Q: For f(x) = x and g(x) = x-6, find the following functions. a. (fo g)(x); b. (g o f)(x); c. (fo g)(7)...

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Q: 2. For g(x) = cos³ (2x - 1), find g' (#). %3D –

A: topic - derivative of a function

Q: 4. S sinºx dx

A: This question can be solved by applying the concepts of integration of trigonometric functions.

Q: Let ro = -a; xi = 0; and x2 = a. Compute the interpolation polynomial for f(x) = -r* using Lagrange ...

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Q: flying horizontally at an altitude of 1 mile and a speed of 480 mi/h passes directly over a radar st...

A: Topic:- application of derivatives

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given point...

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Q: What are the dimensions of the lightest open-top right circular cylindrical can that will hold a vol...

A: Here volume of the can is equal to the volume of the cylinder. So volume of the can can be expressed...

Q: Find the directional derivative of f(x, y, z) = xy + z at the point P = (2, –6, –-1) in the directio...

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Q: It is known that x>5000. Find the least positive integral solution of the system of congruence equat...

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Q: Use the Chain Rule to evaluate the partial derivative ah at the point (q, r) = (1,2), where h(u, v) ...

A: ∂h∂q=(∂h∂u×∂u∂q)+(∂h∂v×∂v∂q)∂h∂q=ev×4q3+uev×r2Substitute q=1 , r=2⇒u=q4=(1)4=1and v=qr2=1×(2)2=4

Q: Find two unit vectors in 2-space that make an angle of 45° with 6i + 5j. NOTE: Enter the exact answe...

A: Solution of question is written in below steps.

Q: farmer who owns a field adjacent to a straight river wishes to fence a rectangular area. No fence is...

A: Given query is to find the dimensions of the rectangle.

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A: In this question we have to find the deaths by AIDS in 2003.

Q: A piece of wire of length 61 is cut into two pieces. One piece is bent into a square and the other i...

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Q: Two variable quantities A and B are found to be related by the equation given below. What is the rat...

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis.

A: Given

Q: Find dy/dx by implicit differentiation cos(x) sin(y) = x2 − 3y

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Q: Evaluate the integral using the following values. '3 '3 x3 dx = 20, х dx %3D 4, dx = 2 1 '1 x dx 13

A: We can find the answer as below.

Q: If y? In(x) = 5, find dy/dx. dy dx

A: This question is based on differentiation with respect to x.

Q: y" +y = 1.

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

Q: A polynomial f (x) and one of its zeros are given. Find all the zeros. 3) f(x) = x* - 6x + &? + 30x ...

A: We have to find roots of polynomial

Q: - f(x) = - f(x) = x-2 g(x) = 5 In x - 2* g(x) = 4x' log, x %3D f(x) = 10* · e*

A: Solution of question is written in below steps.

Q: Help

A: Topic:- simplification

Q: Find the absolute extrema of the function f(x,y) = xy - x - 3y on the triangular region with vertice...

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Q: Find dy/dx at the given point without first solving for y. x2 — бу — 37 %3D0 at (1, -6) | dy dx

A: This question is based on derivative.

Q: If ye – 6y = 5, find dy/dx. dy %3D dx

A: yex-6y=5y(ex-6)=5y=5ex-6Differentiate w.r.t x

Q: Evaluate the following integral using partial fractions: x - 1 dx x3 + 2x2 – x- 2

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Q: beter minc patiCular solution

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Q: CABA CITY Bonus Problem: 15. Find the slope of the tangent line to the ellipse 4x2 +3y² = 16 at the ...

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Q: Find the directional derivative of f(x, y, z) = xy + z° at the point P = (3, –2, –1) in the directio...

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