Find the derivative of the following functions. Whenever possible, express answer in factored form. 1. y=3x²-3x +7x²-5x²+x-8

Q: Let f(x) f'(x) (6x-2)4 (5x2 – 4)6 . Compute f'(x).

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Q: Find the derivative of the function. 3 5)³ - (₁ y = 8x²-5 4-X

A: y = (8x2 -5/4-x)3  we have to find dy/dx here we use chain rule and make differentiation d(u/v)dx =…

Q: Write the function, y = |x| after the following transformations: 1) Reflect the function about the…

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Q: Calculus Distance between point P (2, -1, -3) and line 11 with equation given by (parametrically): {…

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Q: y (3x² + y²) dx + x(x² + 3y²) dy = 0

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Q: Problem 5. Find in two ways: (a) (b) (c) S sin 2x dx Using the u-sub u = 2x. Using the identity sin…

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Q: 4. y= 4-9x 4+9x

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Q: 7) Write the algebraic representation for the given piecewise function, using function notation. (…

A: When x≤1f(x) is the upward parabola with vertex (0,-2)

Q: 5) For the function f(x)=3√2(x-5)+8 , state the domain and range of f(x) and f'(x).

A: Let's find domain and range of given function.

Q: Use the graph off to determine each of the following (a) the domain off (b) the range of f (c) the…

A: We need to find out the domain, range, zeros etc for the given graph of the function.

Q: List the first five terms of the sequence. n³ - 9 a₁ a2 a3 a4 a5 = = = = an = n OLL

A: Solve the given

Q: 1. Evaluate lim h→0 if f(a+h)-f(a) h f(a)= a² - 4a +6 2(a+2) O2(2a-1) O4a-2 2a-4 None of the Choices

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Q: Question 6 Given f(x)=√, g(x)=x²-1, x > 0. Find the value of f (g (3)). O 2√8 O (E) O 2√2 O√3

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Q: Find an equation of the parabola with vertex (-2,-2) and directrix X=1, U 09 0=0 9

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Q: lim 1 t-> +→> -∞0 17 + cot = ² +

A: note that cot^-1(- infinty)=0

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: 1.  Given the function y = x⁴-2x²: DETERMINE THE MAXIMUM POINTS,  MINIMUM POINTS, AND INFLECTION…

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Q: Compute the partial derivatives: z = ln(x3 + y7) о дz ?x Oz ду || о

A: Given query is to find the Indicated partial derivative.

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: Let f(x) = (3x + 7)(3x² + 2)8. Compute f'(x).

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Q: Let f(x)=xsin(x)/1+x. Find f'(pi/2).

A: We can find the answer in the below steps.

Q: Evaluate the following integral. S S e 5x e 5x 5x e +6 5x+6 -dx -dx = ***

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Q: A right circular cone with radius r and slant height / has surface area given by A = nr² + nrl. When…

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Q: allons/minute (gpm) into the tank. Water discharges through an outlet in the tank, but this only…

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Q: Find and for the following function. дх ду 3 f(x,y) = x³ - 5xy - 9y²

A: Given function:- fx,y=x3-5xy-9y2

Q: Find the distance between the skew lines =(4,-2,-1)+1(1,4,-3) and F=(7,-18,2)+u(-3,2,-5).

A: Given lines:- l1:r→=4,-2,-1+t1,4,-3 l2:r→=7,-18,2+u-3,2,-5

Q: If z = (x + y)e" and x = u² + v² and y = u² — v², find the following partial derivatives using the…

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Q: 3. lim_ log₂ (x) x-15 4. lim (cos(x)-1)

A: answer 3 and 4 only Given :3.limx→15log2x4.limx→0cosx-1x

Q: Write a simpler function that agrees with the given function at all but one point. Then find the…

A: Given, limx→0x4-5x2x2

Q: Given two differentiable functions fand g, the derivative of the function f(x) - g(x) can be…

A: Given:- f and g are two differentiable functions

Q: Directions: Consider the following function f(x). Part 1 - Difference Quotient That is: If h = 0,…

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Q: y = 8e4x

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

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Q: 7 Calculate (4x + x²) dx, given the following. 40 [(42+x²) 2 √x²dx 2 335 3 8 |-- dx = 7 S(4x + x²)…

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Q: Find the equation of the normal line to the curves at the  point of tangency, if given.  1.…

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Q: 6. y = 3x - st

A: Given :y=3x-15x3

Q: 4х + Зу For the function h(x,y) = · 3ху -2' əh əh find and дх ду

A: Given query is to find partial derivatives.

Q: The point P(3, 20) lies on the curve y = x² + x + 8. If Q is the point (x, x² + x + 8), find the…

A: Given P(3,20)y=x2+x+8Q(x,x2+x+8)

Q: tan 2x lim 3 X-0 X + a 2 X sin bx X = 0

A: Topic:- calculus

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: 10. S π/2 cos x dx (sin x)√√sin²x-(1/4)

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Q: General solution 1. y = cx+c²+1 2. y² = 4ax 3. y = 4 + ce³x dy dx Answer (ODE) y=xy' + (y)² +1…

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Q: √√2 7. So 0 dx √ 2 4-x²

A: We need to find out the integration.

Q: 2. So x+1 (x² + 2x + 6)² dx

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Q: A Cepheid variable star is a star whose brightness alternately increases and decreases. For a…

A: Given, B(t)=3.0+0.25sin2πt5.2

Q: 3. The profit of a certain cellphone manufacturer can be represented by the function p(x) = -2000x²…

A: p(x) = -2000x2 +12000x +126000 this is profit equation is given  for make maximum profit we have to…

Q: Solve ABC subject to the given conditions. A 10.5°, C 97.1°, b=62 Part: 0/3 Part 1 of 3 B 11 O X $

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Q: Information is given about AABC. Determine if the information gives one triangle, two triangles, or…

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Q: Find the equation of the tangent plane to the surface determined by at x = 3, y = 4. 2 = x¹y¹ + z =…

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