In(a) = 2, ln(b) = 3, and ln(c) = 5, evaluate the following: (a) In () = (b) In √b¹c²a-2 =

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A: Topic:- application of derivatives

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Q: The function is neither increasing nor decreasing. (x)=x+5x+3 O False

A: Topic:- function And application of derivatives

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

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Q: Answer the following Questions: 1. Evaluate the integral using partial fractions method: ²+1)…

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Q: Question 2 Find the oblique asymptote of the graph of y = Oy=x+1 y=x+4 Ⓒy=x-3 Oy=x-1 y=x x²+2 2-1

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Q: Find the derivative of the function. -0 f'(x) = f(x) = (2x - 5) 4(x² + x + 1)5 x

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A: need to find out the solution.

Q: Calculate, to four decimal places, the first ten terms of the sequence. n *₁ = 1 + (-)"

A: We need to find out the first ten terms of the sequence.

Q: First the pieces: 25 5353 7 23 SS 8z as by And putting it all together: dz dz dy dr Ot dy Ot

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Q: Find fx and fy, and evaluate each at the given point. arctan(ỵ), (2,-2) f(x, y) fx(x, y) = fy(x, y)…

A: Given:        fx,y=arctanyx , 2,-2     fxx,y=∂∂xarctanyx                   =1yx2+1∂∂xyx taking y as…

Q: Determine the area of the region bounded by two the curves f(x) = x² – 22x + 48 and g(x) = 11x + 24.

A: Topic = Area

Q: 50. y = x¹/x

A: To find : Derivative of the function y=x1x Take logarithm to both sides, we get logy=1xlogx …..(1)

Q: Find the derivative of the following function. x cos ¹1¹(7x) O O о O 7x √₁ 1 – 49x² 7x √1 − 49x² -7x…

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Q: Let f(x) = x( 1 — [1]) and g(x) be any function. Prove by epsilon-delta definition that lim g(f(x))…

A: Limit

Q: The area under the curve y= 7x bounded by the lines x = 8 and x = 17 above the x-axis is = Square…

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Q: Find the derivative y'(x) implicitly for the equation y' (x)= 4-2y 4x +3 y 2x + 1³.

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Q: given a price-demand function,  p(x) = −7x + 40,  where x is the number of items made and sold and…

A: Given query is to find the revenue function.

Q: 2-x 2 +5 1 dx

A: Given, ∫2-xx2+5xdx

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A: The given series is (3/8)3k, k from 2 to infinity. Repost the next question.

Q: = Find a and b so that f(x) is continuous if f (x) = O O a = ¹/2 b 11 a = EE O a= b = 60 7 a = - 96…

A: A function if said to be continuous if its graph has no break on its domain of definition.

Q: is the relation defined by the table a function of x

A: If each input value leads to only one output value, classify the relationship as a function. If any…

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Q: Based on the data shown below, calculate the regression line (each value to two decimal places) y =…

A: Here for the given values.The best fit values for the regression line are- Slope =1.106 ± 0.08099…

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Q: limx→4 x²-4x √I-2 ||

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Q: Find the partial derivatives of the function fz(x, y) = fy(x, y) = 1 f(x, y) = 4x 2y 1x + 2y 1

A: Given: Now, fx(x, y)=∂ ∂ x4x-2y1· x+2yTreat y as a constant             =∂ ∂ x4x-2y1· x+2y-∂ ∂ x1·…

Q: 2 16. xy = √√x² + y²

A: Given Equation:- xy=x2+y2

Q: A particle moves along the x-axis so that at time t 0 its position is given by x(t) = −t² − 2t + 35.…

A: solution:-particle's positionx(t)=-t2-2t+35where t≥0particle velocityv=ddtx(t)=ddt-t2-2t+35v=-2t-2

Q: Plot the solution using matlab a) Method of Undetermined Coefficients: The differential equation…

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Q: A function and its graph are given. Find the domain. f(x)=-1-√√9-x² 54

A: Ye

Q: 100 Determine, with full justification, if $19 da converges.

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A: We knowLinear approximation Lx≈fa+f'ax-a

Q: 5 Invert the matrix A 8/1+10/2+713 = 0 511 + 912+4/3 = -9 = 1. 91+11/2+8/3 8 10 7 594 9 11 8 and…

A: Please see the below picture for detailed solution.

Q: K Find the linearization L(x,y,z) of the function f(x,y,z)=√2+²+2 at the points (2,0,0), (5,6,0),…

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