Consider the following functions. f(x) =x+7² g(x) x + 7 5x - 7

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Q: 4. G(x) = n x3.4 -5me + p 5. F(x) = ax³ bx² + cx - d 6. f(x) = (3x + 1) (2x7 - x + 2)

A: I am attaching image so that you understand each and every step.

Q: let a and b be integers such that 7 divides both a+3b and a-2b. Show that 7 divides a

A: Given 7 divides a+3b and a-2b  Then 7 divides (a+3b)+(a-2b)= a+b  And 7 divides (a+3b)-(a-2b)=5b…

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: 10) Solve the following and write the intervals. a. C. \7p+4\_ 8 4+3|x-1|>=10 b. d. 2-5|5m-5|=-73…

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Q: Consider the functions f(x) and g(x), for which f(0) = 5, g(0) = 6,ƒ' (0) = -5, and g'(0) = -2. f(x)…

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Q: Let f(x) be a continuous even function, and g(x) be a continuous odd function. Suppose that:…

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Q: At what points is the function y= X+7 2 x² - - 8x+7 continuous? Describe the set of x-values where…

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A: The function is given by y = x3-23x2+4 To determine: The derivative of the function.

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A: Evaluate the definite integral  ∫2e3tdt

Q: Use E-N verification to prove that - →>>> O as n. Vn

A: the answer is in step 2

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A: Given P(3,20)y=x2+x+8Q(x,x2+x+8)

Q: General Direction: • Evaluate the limit of the following transcendental functions using TABLE OF…

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Q: 4. y=x+c₁e* + C2e-* y" -y + x = 0

A: Since you have posted multiple question, I can do first question as per our company guidelines.…

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: 1. Solve the following IVP and find the interval of validity for the solution. y = 5y +e-2xy-2, y(0)…

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Q: (3y2+5x2) dx dx + 2xydy=0

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Q: 2. (a) Let==1-i. (i) (ii) Plot the position of on an Argand Diagram. == Express in the form = = ae¹,…

A: solution

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

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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: SOLVE STEP BY STEP IN DIGITAL FORMAT PLEASE Derive the following functions 38. y=(x²-2x+5)(x²+2x+5)…

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A: Topic:- application of integration

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

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Q: Find an integrating factor for the D.E. (2xy³ – 2x ³y ³ − 4xy² + 2x) dx + ( 3x²y² + 4y) dy = 0

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Q: 3 dx - (3xsiny + 2ysiny-2) dy=

A: Let's solve given differential equation.

Q: Solve for the particular solution: 4e-32-2 y = e-6x +3e-3x+2 ; y(0) = 1

A: Given differential equation  y'=4e-3x-2e-6x+3e-3x+2  ; y(0)=1 Rewrite the differential equation as…

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: The graphs of y = f(x) and y = g(x) are shown below. If g(x) = af (b(x − h)) + k determine he values…

A: The graphs of y=fx and y=gx has been shown above.Given that,  gx=afbx-h+k, we need to determine the…

Q: 0.016t The population of a town is increasing at a rate given by P'(t) = 34 e where P is the…

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Q: General Direction: • Evaluate the limit of the following transcendental functions using TABLE OF…

A: limx→ -142x

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Q: 89. y √3+ Vy 1- √5 3 √r + √2 5 95. Vx² + 1 - x 91. 91-96 Rationalize Numerator Rationalize the…

A: 94) [sqrt(x)-sqrt(x+h)]/[h sqrt(x) sqrt(x+h)].   95) sqrt(x2+1) -x 96) sqrt(x+1) - sqrt(x).

Q: Laplace Transform Determine if the following functions are of exponential order (show complete…

A: 1) t3 sin(2t) 2) 1000 e2020t.

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: 2. Determine dy/dx of the following equation. y = a. C. dy dx = dy dx Cees || ees e2 ee² e O b. dy…

A: See this solution in below.

Q: 2 12. S', [|x + 2 + 1] ²¹ dx | X -4

A: The objective of the question is slove the definite integral.

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: S Radoptimal 5 find the limit and deternue of the functio is continous at the poult buy et…

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Q: 1. Given the piece-wise defined function f(x) = {* a) lim f(x) = x², x < 4 (x+6,x ≥ 4 b) lim f(x) =…

A: Given query is to find the limit of the function

Q: How does the x^4 and the 3x^3 become to 4x^3 + 9x^2. I understand how you got 4x^3 but not the 9x^2.…

A: We know, d/dx (m*xn)=mn(x)n-1 for any real numbers m,n