1. y=√√3x²-5x+

Q: Solve the DE dy/dx + (2/x)y = 6x³.

A: Given,            dydx+2xy=6x3To find : Solve the DE.

Q: y = x(2x + 1)³, find y".

A: Topic = Derivative

Q: Find the derivative of the following functions. Whenever possible, express answer in factored form.…

A: Given y=3x2+43

Q: Find the scalar equation of the line = (-3,4)+1(4,-1)

A: Given query is to find the scalar equation of the line.

Q: 3 If f(x) = 2x√x + ²√ find f'(x).

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Q: For the constant numbers a and b, use the substitution a = a cos² u + b sin² u, for 0 <u<, to show…

A: Given data:- x=acos2u+bsin2u ∫dxx-ab-x=2arctanx-ab-x+c

Q: Compute the partial derivatives: ?х 8z dy || 8x

A: Given that , z=8xx2+y2 find the partial derivatives.

Q: b) lim 818 c) lim 818 2x³-3x+1 3x4+7x³-2x-1 sin (x+3) X

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Q: Find the derivative of each function using the basic properties of differentiation. 1. f(x) = 5-7x…

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Q: Determine the parametric equations of the plane containing points P(2, -3, 4) and the y-axis.

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Q: Find the function y = f(t) passing through the point (0, 10) with the given differential equation.…

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Q: G(r)=3r^3/2 + r^5/2 /r  *differentiate the function How do I approach problems like this? Like…

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Q: y=3e^x + 4/∛x *differentiate the function.

A: Topic:- derivatives

Q: Evaluate the integral. (Use C for the constant of integration.) [√ cos(6) sin³ (8) de

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Q: dx 1 9+(x+2)² 7 8. S₁

A: We need to evaluate integral.

Q: Finding the Domain and Range of a Function: f(x) = 2+4 Domain: all x 2 Range: all y-1 Domain: all x…

A: Solve for domain and range

Q: Define g(-5) in a way that extends g(x) = x² - 25 x + 7x + 10 to be continuous at x = -5.

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Q: e selling price of a refrigerator, is $678.70. If the markup is 10% of the dealer's cost, what is…

A: Given query is to find the dealer's cost.

Q: Evaluate the definite integral. Give the EXACT ANSWER. (no decimal approximations) 4 (2x²-4) dx =

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Q: 4. An object is moved along the line from the point (1, 2, 1) into the origin (distance is in…

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Q: Consider the following. dt ho √ 16+ ² Let t = 4 tan(8) and determine the following. dt t-0-8= t=4-8=…

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Q: Find the derivative of the following functions. Whenever possible, express answer in factored form.…

A: Given  y=3x5-3x4+7x3-5x2+x-8 We know that d(xn)dx=nxn-1

Q: II. Find the equation of the normal line to the curves at the point of tangency, if given. x²-4 x +1…

A: (2)   y=x2-4x+1   at     the   point   (0,-4). Quotient  Rule If f(x) and g(x) are differentiable,…

Q: determine an equation in factored form for a polynomal function with zeros -1 (order 2) and 3 (order…

A: zeroes -1 (order 2)  :  factor ( x+ 1 )2 3 (order 3)  : factor ( x - 3  )3

Q: What rational function satisfies these conditions? lim f(x)=10 (x-->3), lim f(x) =2 (x--->…

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Q: Evaluate the indefinite integral: dx S x In 7x +C

A: Let ln7x = t

Q: 10) (2+8)+10² +60÷10

A: BODMAS Rule As per the BODMAS rule, we have to solve in the sequence of Bracket, Order(Powers),…

Q: Q1. Find Domain and Range of у sin(x)

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Q: Find the third derivative of f(x)=^3sqrt(9x+1)

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Q: y = 3x³-2 5x243

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Q: Find the formula for the graph of the function f(x) given in the graph above. f(x) = 5sin(pix)+2 AN…

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Q: Problem 1. Determine whether each of the following statements is true or false. If it is true,…

A: (a) The first statement is integration by parts reverse the chain rule.

Q: дz Use implicit differentiation to find and 3, Əy дz ?х

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Q: 1. Find the equation of the tangent line to the given curves at point of tangency, if given. 2. y =…

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Q: Below are the graphs of 6 functions A-F. There are also graphs of 5 derivative functions 1-5. Match…

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Q: Calculus Find the volume of the solid generated by revolving the region bounded bythe graphs of y=x,…

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Q: If f ( x ) is a linear function, f ( − 2 ) = 0 , and f ( 3 ) = 2 , find an equation for f ( x )

A: We have, f-2 = 0f3 = 2 To determine: The expression of fx if it is a linear function.

Q: Please kindly explain the steps and the answers are not clear. Can't really tell what's going on.…

A: Let's solve for function.

Q: Consider the following functions. f(x) = 4x + 6, g(x) = 5x - 1 Find (fog)(x). Find the domain of…

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Q: Find the equation of the tangent plane to the surface determined by at x = 3, y = 4. z = x¹y¹ + z −…

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Q: Find the dimensions of the rectangular dog park split into two pens (sharing a fence ) of the same…

A: Let's find dimensions.

Q: solve  log10(x+3)-log10 X =1

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Q: =O 2. (6x+y²) dx + (2xy-3y²) dy

A: Given differential equation, (6x+y²)dx+(2xy-3y²)dy=0...(i) Comparing (i) with Mdx+Ndy=0 we get,…

Q: Find the derivative of the following functions. Whenever possible, express answer in factored 3.…

A: y=(x^3-6x)(2-4x^3) apply product rule y=uv dydx=udvdx+vdudx

Q: 13limx

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Q: 5. Find the second derivative of f (x) (x² + 1)³.

A: Given query is to find the second derivative.

Q: Free fall. In dropping a stone or an iron ball, air resistance is practically negligible.…

A: Given     Acceleration of gravity, g=9.80 m/sec2=32 ft/sec2 At t=0, v=y'=0

Q: 8. After p practice sessions, a student could perform a task in T (p) = 36(p + 1) 3 minutes. Find…

A: After p practice sessions, a student could perform a task in T(p) = 36(p+1)3 minutes We have to find…

Q: Prove that square root 3 is not a rational number.

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Q: ax b.) Find explicit solution for the given initial-value problem (b₂)} \ 1 + x²) dy + × ( 1 + 4y ²…

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