Learning Activity 1: Determine the general antiderivatives of the following functions: 1. f(x)=6x5 - x4 + 2x2 - 3 MD 2. f(x) = -3 3. g(x) = x3-3x² + 3x- 1

Q: Given the curve X = 2y – y and the line X = 0 Find the moment of R with respect to the y-axis M. y…

A: Given problem:- Given the curve x = 2y-y2 and the line x = 0 Find the moment of R with respect to…

Q: If the partial fraction decomposition of 2s2+13s–17 A s+3 Bs+C s2 –2s+4 (s+3)(s² –2s+4) then, the…

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Q: (b) Evaluate each of the following integrals ) || sin(z+ y)dzdy where R= |0,1] × [0,1] (i) evdA…

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Q: Use the form of the definition of the integral given in this theorem to evaluate the integral.

A: Topic:- definite integration

Q: eventually

A: We will solve the problem.

Q: Sx5 V16x6 – 24.x3 + 9 dx

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Q: (i) B(2,3)-

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Q: Find fxy(x,y) if ​f(x,y)=(x^3+y^4)^7. fxy (x,y) =

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Q: S: Solve: do Sinho t cosho

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Q: Find the volume of the solid that results when the region enclosed by the curves y=x², x=y² is…

A: Given:      Curves y=x2                  x=y2 Volume of solid V=∫abπfy2-gy2dy    Here fy=y…

Q: Find the area (in square units) of the region enclosed by the curves y = x3 - 4x2 + 3x and the…

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Q: What are all values of x for which the function f defined by f (x) = a+3z2 - 9x +7 is increasing?…

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Q: 1. The direction vector of a line is an indicator of its slope. 2. The dot product of two vectors…

A: Basically we know that direction of a vector is the angle made by the vector with the horizontal…

Q: (-2)2n is En=1 00

A: ∑n=1∞-22nnn

Q: Find the area of the region bounded by the graphs of y2 = 5 – x and y2 = 4x.

A: Given y2=5-xy2=4x

Q: 3. a) Describe the translations applied to the graph of y= x² to obtain a graph of the quadratic…

A: The given quadratic function g(x)=3x+22-6

Q: Hemegeneus y= JーX

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Q: Find the first five non-zero terms of Maclaurin series (Taylor series centered at a = 0) for the…

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Q: 2x + 3 dx 4x2 – 4x + 5

A: The objective of the question is evaluate the indefinite integral.

Q: 5. а. ³(1 + t4)³ dt

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Q: Use implicit differentiation to determine dy/dx given the equation x^5+y^2=−4

A: implicit differentiation to determine dy/dx given the equation    x5+y2=−4

Q: epresent the following equation in ?² by a vector-valued/parametric equations: 2?² + 2?² − 2? + 2? =…

A: answer is in next step Represent the following equation in R2 by a vector-valued/parametric…

Q: Determine by direct integration the centroid of the area shown in the figures. Where a= 22 cm and b=…

A: The centroid of the bounded region: The centroid x¯-y¯ of a region bounded by the graphs of the…

Q: A tree trunk has a circular cross section at every height; its circumference is given in the…

A: Let's find.

Q: 3. a) Describe the translations applied to the graph of y= x² to obtain a graph of the quadratic…

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Q: Problem 3 T A. N is rotated 3n radians. Mark the point where it is located as A. YA B. N is rotated…

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Q: 2ª + e2" sin(2ª) dx sin(2ª)

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Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

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Q: i cant seem to understand the answer. could you please retype or send a picture?

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Q: Find the area bounded by the curves y 6x - xand y= x -2x A) 128/3 B) 57/3 C) 64/3 101/3

A: Given problem:- Exit the area bounded by the curves y=6x-x2 and y=x2 -2x

Q: Use the substitution x = 3 sin t to evaluate the integral f V9 – x² dx. | Note: Use C for an…

A: Given; I=∫9-x2dx   ...1   Use the trigonometric identity; 1). sin2x+cos2x=1 2). cos2x=2cos2x-1 And…

Q: Solve the initial value problem for r as a vector function of t. dr 9 Differential Equation: diz+…

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Q: Solve for x by converting the logarithmic equation to the exponential form. log(x) = 4 x=_____

A: log10x=4⇒x=104⇒x=10000

Q: A linguist studying the spread of new words and slang observed that the number of daily occurrences…

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Q: Evaluate the integral In(x) le2 x[ln4(x)-1] e3

A: The integration of the integral is  ln(x)/[x(ln4x -1)] limit from e2 to e3.

Q: a) Is the series >. is Vn + n3 + 10 n=1 convergent or divergent? justify your answers. 8.

A: We have to find the convergent test

Q: Find fxx​(x,y), fxy​(x,y), fyx​(x,y), and fyy​(x,y) for the following function.…

A: To find fxxx, y, fxyx, y, fyxx, y and fyyx, y for the following function.fx, y=3x2y2+4x3+6y

Q: blem #1: Differentiatef (x ) = [(4 x4 -5 )(3 x2-9 x - 5 ) ]3 and solve f (2).

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Q: Problem #6: Find the equation of the line tangent to f (x)= cos x-sin? 1 at x =-. 5х 6.

A: We have to find out the tangent line

Q: State the discriminant of 6x2-2x+K

A: Quadratic equaton is  6x2-2x+K=0

Q: Using the key matrix A = decode the message: 36 50 53 76 29 34 15 22 37 64 (Note: Use 27 for space…

A: Concept: Matrix: A matrix is a row-and-column mathematical structure. The Aij element of a matrix,…

Q: 16. lim (2 – 3x) = –4 %3D

A: Concept: Epsilon-Delta Definition for Limits: The Epsilon-Delta Definition for Limits, also known as…

Q: dx 3. I 32x 4. J sin x tan x dx dy 5. J gy²+6y+5

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Q: Find the derivative of the function at Po in the direction of A. h(x, y, z) = cos xy + e + In zx,…

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Q: The position of a particle in the xy-plane at time t is r(t) = (t - 1) i + ( - 2) j. Find an…

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Q: Find the equation for the plane through the points Po(0,2, – 5), Qo( - 4,1, – 4), and Ro(5,4, – 3).…

A: plane passing through the points P00,2,-5, Q0-4,1,-4 and R0=5,4,-3

Q: The volume of water in a right circular cone of base radius 6 inches and height 18 inches decreases…

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Q: Assume that the radius r of a sphere is expanding at a rate of 70 cm/min. The volume of a sphere is…

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Q: 8 – x2 dx I. x(x2 + 5x + 8) 1

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Q: Kndly answer immediately   If f ‘(x) > 0 for all x = (a, b), then function f in the interval is a.…

A: topic- derivative of function