Use logarithmic differentiation to find the derivative of the given function. = (3x² +7²)² (x−³ − 1)³ y =

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Q: Evaluate f 1 x-2x³/4-8√√T da by substitution of a = u and then partial fractions.

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Q: Sketch the graphs of the following functions. 9. f(x)=x³-6x² + 12x-6 10. f(x) = -x³ 12. f(x)= x³ +…

A: Sketch the graphs of the some given function. 9) f(x)= x3 -6x2 +12x-6 11) f(x)= x3+3x+1 13) f(x)=…

Q: Given f(x) = 3 sinx, determine the value of c on (0, - 2 by the Mean Value Theorem. c Ex: 1.23…

A: Topic - Mean Value theorem We are given, f(x)=3sin x  ,  0,3π2 We know that ,by mean value theorem…

Q: a set of parametric equations for the tangent line to the curve of intersection of the surfaces at…

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Q: 3. Give the value of (a) P (10, 1) (b) P (10,0) (c) P(10,-2) + P(10, 17) (d) P (100, 40)/P (99, 39)…

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Q: Given that f(x) (a) (f + g)(3)= (b) (f - g)(3)= (c) (fg)(3)= (d) (-) (3)-[ = x² - 7x and g(x) = x +…

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Q: Find the rate of change of a population of size P(t) = ³ + 4r + 10 at time! = 4. The rate of change…

A: P(t)=t^3+4t+10         rate of change=dP(t)dt             dt^ndt=nt^n-1

Q: If f(x) = 7 sin x + 10 cos x, then f'(x) = f'(3) = (round to 3 decimal places)

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Q: Consider the function: f(x)=7x+1 Step 2 of 2 : Find the value of f(a+5)

A: Consider the function: f(x)=7x+1Step 2 of 2 :   Find the value of f(a+5).

Q: Which of the following statements imply that thas a vertical asymptote at ? Make sure to select the…

A: We have given the function g(x) and the vertical asymptote at x=3.

Q: Question & Determine which of the following tests would be best to use to determine the convergence…

A: Solution: ∑n=1∞1ln(n) Applying Integral test If there exists an N≥k so that for all n≥N, f(n)=an is…

Q: Graph the following. 0 0 peacewise function. +£3. 3≤ t < 5 + 25

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Q: Write an equation for a rational function with: Vertical asymptotes at x = -2 and x = -4 x…

A: Here vertical asymptotes at x = -2 and x = -4 we have denominator (x+2) and (x+4) as co-factor .…

Q: Operations on Functions Using Tables of Values Use the graphs for f(x) and g(x) to evaluate the…

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Q: Find an nth degree polynomial function with real coefficients satisifying the given conditions n=3…

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Q: Evaluate the integral. [²3 0 x In (3x) 4 dx

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Q: : : 2. Find the area above the x-axis bounded by the function f(x) = -x² + 2x + 3 and the x-axis.

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Q: 5. Let U(x, y) be the utility function for two goods, X and Y, given by xy² x- Y U au au Find the…

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Q: Find the derivative of the function. y = In(xvx²-8) y' =

A: y=lnxx2-8 Apply Chain Rule

Q: Letū= (-2,37₁ v = (-5,27 and W = (-2₁4) Find the vector X that statif statisfies in this X = 1…

A: See this solution in below.

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A: Consider the given graph:

Q: QuestivII Determine which of the following tests would be best to use to determine the convergence…

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Q: A factory manufactures three products, A, B, and C. Each product requires the use of two machines,…

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Q: Use logarithmic differentiation to find dy dx y = (x + 1)(x-6) (x - 1)(x+6) dx X>6

A: By using logarithmic differentiation to find dydx.y=x+1x-6x-1x+6, x&gt;6

Q: Find the length of arc of the curve given by the parametric equations: x = t³, y = 2t², −1≤t≤2.

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Q: Consider the following. 11.4 (4x-y) dA, where R is the region in the first quadrant enclosed by the…

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Q: Evaluate the definite integral. Your answer will be a function of a. - 8t + 5) dt =

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Q: Find the linear approximation of f(x)=ln⁡x at x=7 and use it to approximate ln⁡(7.05).   L(x)=? x +…

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Q: If sin x 3 5' (without finding x) sin(2x) cos(2x) tan (2x) = = = x in quadrant I, then find

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Q: Find the critical point(s) of the function f(x, y) = x¹ +y¹ − 40xy. Enter your answer as an ordered…

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Q: Let S be the solid inside the sphere x2+y2+(z-3)2 = 9 and the below the cone x2+y2 = z2.   Setup…

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Q: For the function f(x) = 3x² - 4x, evaluate and fully simplify each of the foll f(x + h) = f(x…

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Q: Determine the sum of the convergent series below. Σ-14 sin" (10°) n=1

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Q: 2. Given that f(x) dx = 6,ƒ(x) dx = 3 and ¹₁ f(x) dx = -1, 1/³ + f(x) 2 find + 6 dr.

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Q: When a quarter is tossed four times, 16 outcomes are possible. HHHH HHHT HHTH HHTT HTHH HTHT HTTH…

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Q: Find a polynomial P(x)=x3+ax2+bx+c satisfying ALL of the following properties: i) x = -1 is a local…

A: f(x)=x³ +ax²+bx+c f '(x)=3x² +2ax+b It is given f(x) is maximum at x=−1, hence f'(−1)=0 ⇒f…

Q: Find the general solution of the equation y'' + 5y' - 6y = 0 Use lower case c₁ and c₂ for the…

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Q: 3. The limits below do not exist. Verify this by showing two different pathways that result in…

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Q: + 1, the x-axis, x = -1, and x = 2. Use the Define R as the region that is bounded by the graph of…

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Q: Find the following limit. lim cot (4x) 24

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Q: f(t) = 5e-7t

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Consider f(x) = − 5x(8 − x)¾ Determine the intervals on which f is concave down. Of is concave down…

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Q: Consider a particle moving along the x-axis where x(t) is the position of the particle at time t,…

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Q: Find the derivative of the function. 9 5-2 +8√x x5 h'(x) = h(x) =

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Q: Air Purification During testing of a certain brand of air purifier, the amount of smoke remaining…

A: Recall Power rule dxndx=nxn-1

Q: Differentiate the given function using the appropriate rule(s). Your answer does not have to be…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: -4z The function f(x) = (7x - 7)e` x = has one critical number. Find it.

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: What is q' (x) when q(x) = ln((x² + 1) (x³ + x² +2))?

A: q(x)=lnx2+1x3+x2+2