malize the vector ₁ || -1

Q: Consider the function f(x) = x² + x and the point (1, 2). (a) Find the slope of the tangent to the…

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Q: Find the equation of the line L that passes throught point P( – 6, 2, 4) and Q( – 3, — 1, 5). - r(t)…

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Q: Question Given that F(x) = 3x5 (1+12) ¹5. dr, what is F'(x)? (Do not include "F"(x) =" in your…

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Q: a. Graph f(x) = 4-x², X#2 = 2. 4₁ b. Find lim f(x) and lim f(x). X-2* x X-2 c. Does lim f(x) exist?…

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Q: How many square meters is the total area of the land? 19 meter 14 meter 4 meter 15 meter

A: Solution

Q: Use the Generalized Power Rule to find the derivative of the function. 9(2) 52(62²-7z+ 1)²

A: Concept: The chain rule has a specific case known as the broad power rule. When determining the…

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Q: Sketch 9x2 + 25y2 = 5625 and the line segments connecting (20, 0) and (-20, 0) to (15, 12)

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Q: 8. y-³ = x³ (3ex + c); xy' + y + x¹y¹ex = 0

A: y-3=x33ex+c

Q: Solve the differential equation. dy COS X + y sin x = sin x cos x dx A y = cos x In | sec x | + C…

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Q: Find the open intervals on which the function f(x)=24x^((1)/(3))(x+9) is concave upward or concave…

A: Given :fx=24x13x+9

Q: Find the acceleration of the specified object. (Hint: Recall that if a variable is changing at a…

A: As shown in given diagram, y is height of right angle triangle, z is hypotenuse of right angle…

Q: Perform the indicated operations on the given vectors: 5 --0--0--9--6) 8, = 4 , -3 4 7 -7 -5 U4 =

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Q: If 6x²y + xy² = 7x, find y' by implicit differentiation. y' =

A: Solution is done in step 2

Q: Use the graph below to determine whether the statements about the function y = f(x) are true or…

A: Topic- Limits and continuity we are given, graph of a function. we know that limit at a point x=a…

Q: The solution set of the system x-y=12 is the set of ordered pairs that satisfy and

A: Given   1. x-y=12

Q: Tutorial Exercise Find the open interval(s) on which the curve given by the vector-valued function…

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Q: Find the parametric equation for the line where the planes 6x + 7y4z = 2 and 8y – 2z = 10 intersect.…

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Q: s Find all values of x that satisfy 1 x-1 ≥100. Use interval notation to answer. Show all work.

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Q: Given f(x) = 3x³ + 2, use a table to estimate the slope of the tangent line to f at the point P(0,…

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Q: 0 A can of soda is placed inside the refrigerator. The soda has an initial temperature of T = 70°F.…

A: I have appended the formula used in the solution part of the question

Q: For f(x)= square root x and g(x)=x-1 find the following function (gof)(x) H HE

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Q: Perform the indicated operations on the given vectors: 3 z - ().- (1). (₁₂₁). () (-³) = , V3 = U4 =

A: Given a vector v1

Q: Find r(t) u(t). . r(t) = (5t4)i ³j+2k u(t)= t²i4j+t³k r(t)u(t)= Is the result a vector-valued…

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Q: I think the second question is wrong

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Q: If x²y³ - 9x sin(y) = 14, find y' by implicit differentiation. y' =

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Q: A bag contains 2 gold marbles, 7 silver marbles, and 25 black marbles. Someone offers to play this…

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Q: Consider the path r(t) = (8t, 4t², 4 ln t) defined for t > 0. Find the length of the curve between…

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Q: Find the derivative of the function using the chain rule (not the "u" version)   *please use…

A: Topic:- application of derivatives using chain rule

Q: Find an expression for the inverse of f(x) = e³x+1. f-¹(x) = 4

A: Topic- functions and inverse functions We are given, f(x)=e3x+1 we know that ln(ex)=x

Q: Problem #2: Evaluate Sfxy ex²164, R where R = {(x,y) | 0 ≤ x ≤ 2, 0 ≤ y ≤ 8}. dA,

A: For the region R , limit of x is x=0 to x=2limit of y is y=0 to y=8

Q: Suppose that f(5) = 1, f '(5) = 4, g(5) = -2, and g'(5) = 3. Find the following value (a) (fg)'(5)…

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Q: Solve the differential equation. dy + 5y dx = e-5x dx A) y = 5x + ce-5x B) y = e-5x (x + c) (C)…

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Q: If x¹ + x²y + 7y² = 14, find y' by implicit differentiation. 2

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Q: Use the Generalized Power Rule to find the derivative of the function. f(x) = F(x)=(x²+1)

A: As we know from the Generalized Power Rule: ddxfxn=nfxn-1·ddxfx The Sum/Difference Rule: f±g'=f'±g'…

Q: x³ + kif x < 4 11 if x 4 kr For what value of k will f(x) be continuous everywhere? Letf(x): 35 O 10…

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Q: Calculus The height of 700 boys are found to approximately follow such a distribution, with a mean…

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Q: log[4.42(±0.01) × 10³7] c. y = d. y = [2.936(±0.002)] ¹/4

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Q: Let f(x, y) = 4√xy² + 4y + eªy. Use local linear approximation to estimate 4√(0.1)(0.9)² +4(0.9) +…

A: Given ;fx,y=4xy2+4y+exyx=0.1 then let x=1y=0.9 then let y=1

Q: Solve the following exact differential equation (yery + 3x²)dx + (xeªy − 7)dy = 0 Express your…

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Q: Experiments show that a colony of bacteria with sufficient food and no predators and with zero death…

A: We need to find time when population triples.

Q: Prove that lim 1 H 101H 818

A: We have to prove that  limx→0- 1x → -∞.

Q: Given the functions f(x) = x2+ 3x, g(x) = √x + 1, and h(x) = 5, find each of the following: (i)…

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Q: Find the general solution of the differential equation xsino d0 + (x³ − 2x²cos0 + cos0)dx = 0

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Q: Solve the differential equations. 1. X 3

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Q: K An exercise machine with an original price of $780 is on sale at 19% off. a. What is the discount…

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Q: For what values of m_and_n_will µ = x¹y™ be an integrating factor for the differential equation (−4y…

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Q: At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 14…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 1. Para la serie de potencias E-01 determina (x+4)" n=0 115 a. El centro b. El radio de convergencia…

A: See this solution in below.

Q: Experiments show that a colony of bacteria with sufficient food and no predators and with zero death…

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