Find the slope of the tangent line to the graph of the function at the given point. y = In x y 10 (1, 0) 4. -5

Q: Find differential of the function y = (x² + 8)3. dy = dx. When x = 5 and dx = 0.05, compute the…

A: Solving

Q: Evaluate the definite integrals using the graph of f (x) below. 6- 4- 2- 4 6. 10 12 -2- -4- -6 3 (a)…

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Q: 6. Which of the following is continuous at all points? B) f(x) = **+2x-35 ズ-5 xマ-4x-5 A) f(x) = x-5…

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Q: Wiedge LE Find an equation of the ellipse that has center (-1, 4), a minor axis of length 2, and a…

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Q: Speedometer readings for a motorcycle at 12-second intervals are given in the table. t (s) 12 24 36…

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Q: 2л 67 xsin 3xsin 2.xdx

A: You have asked multiple questions and not mentioned about which question answer you need so…

Q: y" + 6y' + 8.96y = 0 y" + 2ny' + 7²y = 0 y" + 4.5y' = 0

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Q: Find k such that the line is tangent to the graph of the function. Function Line f(x) - kx y = Sx +…

A: The line is tangent to the given function then , there are two conditions :(1)  The function and the…

Q: The size P of a certain insect population at time t (in days) obeys the function P(t) = 100 e 0.09t…

A: In multiple question we are allowed to answer only first three sub parts

Q: Determine whether the series converges absolutely or conditionally, or diverges. 00 (-1)^ + 1 Σ n +…

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Q: can

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Q: 3. According to Newton's cooling law, the rate of cooling of a hot body is pro- portional to the…

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Q: In a certain bacteria culture the rate of increase in a number of bacteria proportional to the…

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Q: Find a positive number a such that the sum of its reciprocal and 5,324 times its square is as small…

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Q: The graph of f consists of line segments, as shown in the figure. Evaluate each definite integral by…

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Q: Find the derivative of the function. Express the answer using positive exponents only. y = (4x5 –…

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Q: Find the second derivative of the function. g(t) =  7 8t6

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Q: Use the Ratio Test to determine the convergence or divergence of the series. (If you need to use co…

A: This question can be solved using the concept of ratio test.

Q: Verify that f has an inverse function. Then use the function f and the given real number a to find…

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Q: Differentiate the function. 5V1 - x y = y' =

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Q: List the critical numbers of the following function in increasing order. Enter N in any blank that…

A: To find: The critical points of the function and then list them in increasing order. Given…

Q: Estimate the instantaneous rate of change at x= 1 for Ax) = /x + 1. a) -2 b) -0.5 c) 0.5 d) 2

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Q: Find the radius of convergence, R, of the series. E 5(-1)^nx" n = 1 R = 1 Find the interval, I, of…

A: We have to find radius and interval of convergence.

Q: Determine whether the infinite geometric series is convergent or divergent. If it is convergent,…

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Q: Determine the simple interest. (The rate is an annual rate unless otherwise stated. Assume 360 days…

A: P= $ 675 r= 7.75%= 0.0775 t= 30 days Since the rate of interest is given per year. Therefore, Time…

Q: Find the absolute maximum and minimum values of f(x) = -(x² + x) interval [-3, 4]. over the absolute…

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Q: Think of four random integers q, r, s, and t selected from 0 through 9. Let a1 = 0.qrst, where q, r,…

A: let as consider four integers q,r,s,t from 0 to 9 then we get a1=0.qrst=0 now if we select four more…

Q: Find an equation of the ellipse having a major axis of length 6 and foci at (-5, 3) and (-5, -1).…

A: Given problem:- Find an equation of the ellipse having a major axis of length 6 and foci at (-5, 3)…

Q: (a) Find the second derivative of the function y = 2x² sin(x). (b) Find the derivative of the…

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Q: r4 1- So ey/Vx dy dx 2.

A: Explanation of the answer is as follows

Q: Find an approximate value for the integral, using the trapezoidal rule w intervals. Round the answer…

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Q: Find a function of the form f(x) = a sin(bx + c) such that the graph of y 6f 5 4 BR E 37 2 2 -2 3 -4…

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Q: Determine the area of the region bounded. Show complete solutions. 1. y = 2x (1 – x), 0<x < 1

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Q: 4 8 Suppose the sequence {b1, b2, b3, ...} is given by {-1, , 9' 27 Which, if any, of the following…

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Q: Use the graph of the function to answer the each question 1. limr-0-f(x) = 5- 2. lim,o+ f(x) = 4 3.…

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Q: The graph models the amount of radioactive element present over the course of a 10-minute…

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Q: The series n=4 is convergent. The term a29 of the sequence {a,) given by 2 3 4 5 5'7'9' 11 is 31 63…

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Q: INTEGRATE BY PARTS /4 2. Sa* x sin 2x dx

A: The given integral,       ∫0π4x sin2x dx

Q: 4x² + 21x + 54 dx x² + 6x + 13

A: The given integral is  (4x2+21x+54)/(x2+6x+13).

Q: Use the Root Test to determine the convergence or divergence of the series. (If you need to use co…

A: =limn→∞ ann=limn→∞ 3n2n+13n1n=limn→∞ 3n2n+13=limn→∞ 32+1n3=limn→∞ 32+03limn→∞ |an|n=278

Q: 4. A thermometer is removed from a room where the air temperature is 70°F and is taken outside,…

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Q: Given the differential equation y' = x2 + y? Take the Implicit Derivative of this function 2 times…

A: Given, the differential equation                                    y'=x2+y2 then take the implicit…

Q: (a) Find an equation of the tangent plane to the surface at the given point. x + y + z = 10, (3, 4,…

A: Let's find.

Q: Use the Root Test to determine the convergence or divergence of the series. (If you need to use co…

A: Root Test : Consider the positive term series ∑ an . Define,         L= limn→∞  ann= limn→∞ an1n ,…

Q: I. Evaluate the following. 3450°-j12 a. 14 + j2 – -j15 (3450°-j12) b. j2 x 32-25° -j15 5-j2…

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Q: y=3 13 x-3-y 3

A: V = 2π∫ yf(y)dy f(y) = 3 -(3-y2) f(y) = y2 +3 -3 now limit from 0 to 3  V = 2π∫03 yf(y)dy V = 2π∫03…

Q: Consider the following. Function Point f(x) = arcsec 5x 4 (a) Find an equation of the tangent line…

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Q: If 0 = then %3D sin(e) = cos(0) = CO: !3! Give exact values. No decimals allowed! V2 With functions…

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Q: Given the differential equation y' = 4y2 + 7 Take the Implicit Derivative of this function 2 times…

A: Consider the equation  y'=4y2+7

Q: y=(x+5)^x Differentiate

A: Solution: y=(x+5)^x dydx=ddx((x+5)x)