. Find the derivative of a composite function using the Chain Rule or General Power Rule. 1.) y=(3x+1)³ 2.) y=2(2x+1)⁴ 3.) y= √(3-t)

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Q: 1 1-x Use the geometric series f(x)= = Σx, for |x|<1, to find the power series representation for…

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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: Directions: apply the limit theorem 3 1. lim x-24 2. lim-45 x-2 62 3. lim x 2 3 4. lim x x-2 5. lim…

A: Please refer to the image below

Q: Convert each pair of polar coordinates to rectangular coordinates 1. (3, 225 degrees

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: The graph of y=f(x) is shown. Draw the graph of y = -f(x). 17 Ex X 3

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: ** Evaluate the following integral. Answer in 3 significant figure, exponential form, no units, no…

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Q: sec x = Let f(x) + x³e² - log₂ (5x + 1) + 1 x² √T Using the derivative rules learned in our course,…

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Q: The total revenue for a product can be calculated as the area under the demand curve. Suppose that…

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Q: please include let u du substitutions

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Q: Evaluate f , rydyda Select one: a. 3 b. 1 C. 2 d. o

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Q: Evaluate the following limits. a. limx→+ 2x 3x²

A: This question is based on limits.

Q: Two cars started at the same point but at different times (of the same day) and at different speeds.…

A: Car A left at 9am travel to west direction at speed 30kph,  Therefore at 2pm car A travel total…

Q: For each graph, choose the function that best describes it. (a) (b) (Choose one) (Choose one)…

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Q: A parabola has an equation of y-32= 0. Compute for the surface area of the solid generated by…

A: Given: y=3x12 At y=0, x=0 The surface area of the surface of revolution formed by revolving the…

Q: ل 13 y=√x 0 Figure A 10. Consider the region in Figure A. Its area may be found using [f(x) =…

A: First, finding the intersection of two curves.

Q: √x³√1-x² x2

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Q: xp h+Z² S Select one: a. Ob. c. Od. In x² +4 + c In 2+2+c ln +4+c In 2+2+c

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Q: 5x5 (a²-x²)6 dx 0

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Q: Without using the graph, determine all critical points of e2x − 2x and classify them as local max,…

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Q: Physical Applications of First-Order Differential Equations A body of unknown temperature is placed…

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Q: 3. Find the equation of the tangent to y = 1-x² 3x+7 at the point where x = 1.

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Q: Find the general equation of the circle of curvature of the parametric equation t+1 X: ; y = ±…

A: This is a problem of finding equation of the circle of curvature. Based on the general formula and…

Q: Find critical points of ƒ(x) = x² ln(x) — 1⁄x² on the interval (0, ∞).

A: Given; fx=x2lnx-12x2 ; x∈0,∞    As we know that; The critical points of the function, y=fx can be…

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Q: Find Value of integral ) dx X+1

A: Given query is to find the value of the integral.

Q: Sº₁ 1 2 x³ dx x²+x+1

A: Solution of given question is written in below steps.

Q: Find the derivative of both a and b a. x csc-1(1/x) b.(esin2x)/[In(cos2x)]2

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Q: y' = X 2 h

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Q: Find the derivative of f(w) = √3w²

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Q: 1. Evaluate the given integral Q. Q - CC² LL- (x - y) dx dy y²

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Q: √x³√1-x² 2

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Q: If f(x) = exy, then f'(x) = yexy xexy-1 Select one: True False

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Q: Find the derivative of the function y = (4x + 1)4(5x + 1)-5. dy (16x+4) 3 (4x+1)4 dx (5x+1)5…

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Q: TC √³x² x² sin3x dx

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Q: If y=u³ and u = 4x² - 2x + 5, give dy dx

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Q: Evaluate the following limits 2x a. limx→>+00 3x²

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Q: If f(x)=√x² - 1, then 0 is one of the critical numbers of f. Select one: True False

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Q: 2. Show that the function g defined by VVT y² + √² 2, is not continuous at (0,0). (z,y) = (0,0)…

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Q: Evaluate the equation for f Select one: a. 0.5 b. -1 Oc. 2 Gd. 1 dzdy

A: Let I=∫01∫yy21y2-x2dxdyLetI=∫01(I2)dy                                    (1)WhereI2=∫yy21y2-x2dxWe…

Q: Sx". .n-1 + n[x²- x" sin x dx = -x cos x + n cos x dx

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Q: NIFN dx √2x (√2x + 9)

A: Given query is to find the value of the integral.

Q: If the sides of an equilateral triangle are increasing at a rate of 6 m/min. How fast is the area of…

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Q: 3. Determine the limit graphically. Confirm algebraically. x - 1 lim x-1 - 1 1² - 3t+2 lim 1-2 1² 4…

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Q: Use substitution to find the indefinite integral. X 1²2* S= 4x² +2 X 4x + 2

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Q: Topic: Arc Length Find the length of the arc of the function x^2 = 4y from x = -3 to x = 3. a) Graph…

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Q: Fermat's theorem states that if f has a relative extremum and if f'(x) exists, then f'(c) = 0.…

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Q: Sx³√4 - 2x² dx 3

A: We have to solve integration

Q: s dx 3x²+2x+5

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Q: (1, -2) (a) The curve with equation y2 = x³ + 3x² is called the Tschirnhausen cubic. Find an…

A: We have to find the tangent equation and draw the graph.