Find the absolute extrema of the function. h(x) = ex2 − 9 on [−3, 3] absolute maximum value: ___ at x= +/- ____ absolute minimum value ____ at x= _____

Q: Find the equation of the tangent line and the normal line of the curves at given point 1. 4x? + 9x?…

A: The given equation,     4x2+9x2=25, 2,-1

Q: 2. Determine whether the following integral is convergent or divergent. Do not guess! 4 dx x2 – x -…

A: To determine whether the following integral is convergent or divergent.∫04dxx2-x-2

Q: V3 - 2s ds 02 40

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

Q: - ſ csc²e cot êī – 5 cot ê dê

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Q: given point 1. y = 2x° - 3x² - 2x + 5 ; where x 1

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

Q: Using the substitution Z=V x+2, the integral xVx+2 dx is equivalent to | 2°(?+ 2) dz 1 | 22?(z?+2)…

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Q: At noon, ship A is 30 nautical miles due west of ship B. Ship A is sailing west at 18 knots and ship…

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Q: 2. The function g(x) is defined for -3Sx5 3. The behaviour of g'(x) and g"(x) is given below.…

A: A)-3<x<-2, g'(x)<0and-2<x<1, g'(x)>0Function decreases over (-3, -2) andincreases…

Q: funchoN f whose second derivative is f ")= 5x+2sin(x If fo 3 and fro)= 3. what is fe?

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Q: 1. Given f(x) S(x) = x² + 4x - 2 and g (x) = 3x – 4 , find the composition of functions for the…

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Q: 1„2 The graph shown is f (x) = ±x². 4 3 21 1 54 3-2 -14 1 2 3 4 5 -2 3 4 If g(x) = `f(t) dt, what is…

A: This is a problem of antiderivative function. Based on the general formula we will answer the…

Q: V25x² -69 – dx

A: We will find the integral as following.

Q: 2x² + 1 Find the lim, f(x) where f(x) : if xs -5 x – 3x-2 if x > -5 x-5* -122/25 O -72/25 O -80 None…

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Q: (a) How far is the boat from the marina? Round the answer to one decimal place if necessary. (b)…

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Q: Find a polar equation in the form r= f(θ) of the ellipse with eccentricity e= 6/7 such that one of…

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Q: Consider the function Z = 2x²(1 – e-) where x and y are given to be 5 and In 5 respectively. Find…

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Q: Let k(x) = tan−1 x. Find the value of k(9)(0), the 9th derivative of tan−1(x) at x = 0.

A: Given

Q: Exact ODE y'=e^(2x-1) y^2

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Q: dx U x" Jx? +3 4

A: To find out the integration.

Q: 1. Evaluate the integral dx Jo x2 + 4x + 20

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Q: Find the slope of the graph of f(x) at the point where the graph crosses the r-axis. pe = Find the…

A: Topic:- application of derivatives

Q: Given the graph of the function below. Find the limit of the functic approaches 3.* (3, 4) (0,3)…

A: Given query is to find indicated limit.

Q: af Given f(x, y) = In(6x² + 8y²) then %3D

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Q: Suppose that enrolment in CLSU has been increasing over the years since year 2014 according to the…

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Q: Determine whether the following statement is true or false. If this statement is true, explain why.…

A: Explanation of the answer is as follows

Q: A stellar object is emitting radiation at 1820 nm. A detector is capturing 7 x 10' photons per…

A: Please refer to the image below

Q: 7. Two functions are defined as f (x) and g (x) = where x * 1. a) Find f (x) g (x). Simplify your…

A: We can solve the given question as follows:

Q: The recurrence relation a,= 6an-1 - 9a,n-2, with initial term ao=1 and a,=6 has a solution, which is…

A: We need to find solution of recurrence relation : an=6an-1-9an-2 with initial term a0=1 and a1=6

Q: Using Integration by parts, evaluate: ſ xVx + 1dx Your answer

A: As per our guidelines we are supposed to answer one question, kindly repost the remaining question…

Q: Suppose the position of a particie is given by parametrc equations x(e) = -3 and y(t) = 2?. (a) Find…

A: The given data is: xt=t3-3yt=2t2  (a) To find the particle's position (x,y) at t=3

Q: Graph the equation below. Choose the correct graph. y = 5.5* OA. O B. OC. OD.

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Q: Consider the following. x = t, y- In(t) (a) Eliminate the parameter to find a Cartesian equation…

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Q: Find the equation of the tangent line and the normal line of the curves at given point 1. y = x V16…

A: Equation of tangent line Consider y=x16+x2slope of the tangent line is dydx  at…

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

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Q: (8x? + 2x) dx = 2x + x? Select one: OTrue O False

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Q: Find the radius of convergence, R, of the series. n- 1 R = Find the interval, 1, of convergence of…

A: We have to find the radius of convergence R for the given series…

Q: Substitution Method dy xy = 0 (7) (x² – y²) (8) 2xy = x² + 2y² - - dx dx (9) (1 1 3r sin v)dr r2 cos…

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Q: Compute the line integral of the scalar function f(x, y, z) = 2x² + 8z ver the curve c(t) = (et, t2…

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Q: wo boats leave a marina at the same time. The first boat travels 8 knots at a bearing of N24°E, and…

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Q: For 5, Sketch the region enclosed by the given curves. Find its area. Make sure you show how you…

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Q: Find the radius of convergence about x = -2 and interval of convergence of the series Sn°(ar + 2)"…

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Q: (sec3x The integral of the given function f (sec dx is \tan3x. cot³3x cot3x + C 3 а. 9 cot3x cot3x…

A: cot2x+1=csc2x sec(x)tan(x)=csc(x) ddx(cotx)=-csc2x ∫xndx=x(n+1)n+1, for any real number n.

Q: Sie cos e sin 20 de t/3 T/6

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Q: Find the derivatives of f(x)=(ax4+b)6   and   f(x)=axe-bx+15 Assume that a and b are constants.

A: Given query is to find the derivative of the expression.

Q: For the function given below, find a formula for the Riemann sum obtained by dividing the interval…

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

Q: 2x + 5 What is true about the function Ax) = X+3 as x → co?

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Q: The integral of the given function f x2 dx is (9-x2)2

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Q: Activity Test your understanding. Write TRUE on the space provided if the statement is correct and…

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Q: a- Described the order of integration when you have a double integration.

A: Simplify the theory.

Q: Find the dimensions of a rectangle with area 216 m² whose perimeter is as small as possible. (If…

A: Find your answer below