function Finding critical points and extreme values: The f(x) = − x(x² − 1) has two stationary points. The smaller is 0 and the larger is 1 . The maximum value of ƒ in the interval [0, 1] is 0

Q: 58. tanx cotx = secx csc x 2 cos x csc x

A: Verify the given identity  tanx- cotx = secx cosecx -2cosx cosecx

Q: Evaluate the limit using L'Hopital's rule 6 cos(7x)sec( – 3x) lim x →

A: limx→π26cos(-7x)sec(-3x)=limx→π26cos(-7x)cos(-3x)cosx=1secxit is 00 form use l'hospital rule

Q: Question Differentiate the series represented by the function f below term-by-term to find the power…

A: Let's find power series of function derivative f'.

Q: Concept check: Evaluate the following integrals: 1. dx (6-x²)z OIL

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Q: Solve the equation (1-5x)e¹-5 =0 for x. Give your answer as an integer or a fraction.

A: lne=1lnxn=nlnx

Q: Differentiate the series represented by the function f below term-by-term to find the power series…

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Q: reference and terminal point of 13pi/4

A: reference angle - angle between terminal arm and x axis let θ = 13π4

Q: nd the first derivative ƒ' and the original function f. f"(x) = x³ - 12x. f'(1) = 0. f(1) = 10

A: Given query is to find the function f.

Q: 1. f'(x) and ƒ' (7). Show all work, no decimals allowed in your final answer y -Cos (x) Tan(x)…

A: Given query is to find indicated derivative.

Q: • f (8. +12) de dx + • / ( 1 + ₁² + 0² - 2²/1) dx [sin(3x)dx

A: (1).The given integral is:∫8-x5+4x dx

Q: Find the volume of the region between the cylinder z = 2y² and the xy-plane that is bounded by the…

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Q: Cartesian coordinates of a point are given. (a) (−6, 6) (i) Find polar coordinates  (r, ?)  of the…

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

Q: Write out the first five terms of the sequence with, [(1 - 7)", determine whether the sequence…

A: To write out the first five terms of the sequence with 1-7n+7nn=1∞, to determine whether the…

Q: 36. a) Find the length of the curve: y = 2 In (sin(x)); ≤ x ≤¶ b) Find the surface area of the curve…

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Q: Find the Taylor polynomials p3 and p4 centered at a=0 for f(x) = (1+x)-³. P3(x) =

A: we will find the required.

Q: 15. f(x, y) In (x + y)

A:

Q: Let - 2x3 - 2y³ - 2z3 + 2xyz - 284 = 0. дz дz Use partial derivatives to calculate and at the point…

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Q: Please show your answers to at least 4 decimal places. Find the directional derivative of the…

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Q: Find and classify the critical points of z = = (x² – 2x) (y² - 5y). Local maximums: Local minimums:…

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Q: Find the Jacobian J of the transformation T(u, v, w) = (-3u +5v-3w, 2u+4v+3w, 4u+v=4w) = (x, y, z).…

A: Given:- Tu,v,w=-3u+5v-3w,2u+4v+3w,4u+v-4w=x,y,z

Q: What is the independent variable in the given differential equation? ду at² O x Oy and t Ot x and t…

A: Given partial differential equation is ∂2y∂t2-4∂2y∂x2=0 We need to choose from correct option about…

Q: the limits of the following questions. (i) lim 1-2x X-0

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

Q: Evaluate the two integrals given the graph. The two parts of the graph are semicircles. 1. 4 f(x) dx…

A: Given both the circles are the semicircles a) ∫14f(x)dx =area between x = 1 to x = 4

Q: K Consider the function f(x) = - (a) lim f(x) = X→∞0 3 4x³ + 18x² + 18x lim f(x) = (a) Evaluate lim…

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Q: Find the solution to the boundary value problem: The solution is y = d²y_6dy + 5y = 0, y(0) = 1,…

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Q: Let 2x² + 5xy - 3y² – 14x − 7y + 20 = 0. dy Use partial derivatives to calculate at the point (3,…

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Q: I For the equation h(x) = -√x+1 a) Complete the table: h(x) x 0 1 4 a b) Use the appropriate tool to…

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Q: Find the limit X / tan 33 ) X X700

A: To evaluate the given limit of the function

Q: 2. A rectangular plot of land is to be fenced in using two types of fencing. Two opposite sides will…

A: Let's find heavy duty and standard fencing should be used so it gives maximum area.

Q: 3. The derivative of a function is given by f'(x) = -63x² - 12x + 18. Give 3 different functions tha…

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Q: (a) Evaluate the following integrals: (i) x²edx (4) J dx (l) J e* sinh (-)dx

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Q: Use the ALEKS graphing calculator to solve the equation. sin 3x=-1.2x+1.4 Round to the nearest…

A: Concept: The graph of the sine function is up and down curve which repeats itself after every 2π…

Q: Sand poured upon the ground at a constant rate of 12 cubic feet/min forms a conical pile whose…

A: The given data is: Sand poured upon the ground at a constant rate of 12 cubic feet/min dVdt=12 cubic…

Q: For the function h(x) = −2x³ - 4x + 3√√x, calculate h'(x), h''(x), and h'''(x) . Show all steps. (2)…

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Q: Find a value of the constant k, if possible, at which is continuous everywhere. k= (enter "none" if…

A: Find the value of k, if possible, at which  f(x)= 16-x2, x≤-4 kx2 , x>-4  is continuous…

Q: If f(x) = 4sin ¹(x²), find f'(x). Find f'(0.7). Round to 3 decimal places.

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Q: Given the vectors v and u, answer a. through d. below. v=7i-3k_u=i+j+k a. Find the dot product of v…

A: Concept: The scalar product of the two specified vectors is referred to as the dot product of two…

Q: xx): 1 + x² For what value of c is f a probability density function? C = For that value of c, find…

A: solution is given below.

Q: Use the figure to evaluate the definite integrals S 2 1 y -1 -2. 1 2 y = g (t) 3 4 +t 5 g(t) dt and…

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Q: Determine if the following sequences converge or diverge. If convergent, find the limit. You must…

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Q: Find df (5x + 2y)dA where R is the parallelogram with vertices (0,0), (-4,4), (3,2), and (-1,6). R…

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Q: 9) Use the Intermediate Value Theorem to prove that there is a number c, such that, Ac)=-1 for the…

A: Given function:- fx=x5-2x3+x2+2

Q: 1. Find the equation of the tangent line to the graph of y=f(x) at x=-1, if fM)=3 and f(x)=ź

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Use the definition of continuity to determine if each function is continuous or discontinuous at…

A: Given function:- fx=x-2x≤-1-xx>-1 Condition to continuity at x=alimx→a-fx=limx→a+fx=fa

Q: 2 Find the exact arc length of the curve y = x over the interval, x = 1 to x = 64

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Q: A vehicle purchased for $25,000 depreciates at a constant rate of 8%. Determine the approximate…

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Q: Sketch the graph of f and use your sketch to find the absolute and local maximum and minimum values…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Optimization problem Steps: 1) sketch 2) label and define the quantities 3) constraint equation 4)…

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Q: In the figure, A(-2,7), B(3,2) and C(9,5) are the three points on the same rectangular coordinate…

A: Let's find slope of given coordinates and then solve for which slope is greater.

Q: Given f (x) = 3x + 2 – 1, what is f –1(x)?  f –1(x) = log3(x – 1) + 2  f –1(x) = log3(x + 1) – 2…

A: