Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = e⁹x + e-x (a) Find the interval on which f is increasing. (Enter your answer using interval notation.) Find the interval on which f is decreasing. (Enter your answer using interval notation.) || (b) Find the local minimum and maximum values of f. local minimum value local maximum value (c) Find the inflection point. (x, y) = Find the interval on which f is concave up. (Enter your answer using interval notation.) Find the interval on which f is concave down. (Enter your answer using interval notation.)

Q: The shaded region shown below is bounded by the functions f, of, x, equals, minus, 3, x, squared,…

A: Given that the region is bounded by the curves and  and the x-axis and the y-axis.

Q: Find the distance from the point (0,1,-1) to the line a(t) = (-2, 2, 4)t + (-6, - 1,5)

A:

Q: Determine the price p (in dollars) that maximizes total revenue. p = $

A:

Q: Find the number k such that there exists a function y which is differentiable at every x and…

A:

Q: 8) Write the expression -3sinx + 4cosx in the form ksin(x + a) for 0 < a < 2. Round a to three…

A:

Q: Need help understanding please and thank you

A: Summary: (7.Answer): arctan(x/2)+C (8. Answer): 2/3 * arcsin(3y) + C  or -2/9 (sqrt. 1 - 9y2) +…

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time interval…

A: Given that the a particle with position  as t varies,

Q: Question 9 Use the given information to find the exact value of the expression. sin α = 1, & lies in…

A: Ans : B  = 25−6+421​​Explanation:Explanation:

Q: Check all of correct statements about differentiable functions. The derivative of the sum of two…

A: We have to identify the correct statement.

Q: Evaluate the derivative of the given function at the given point. y = 2x³-3x² + x + 8; (1, 8)

A:

Q: A. Find S'(t) B. Find S(20) C. Find S'(20)

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Find dy dx if y = √Inx +1. 1 dy dx 2 x √In(x)

A:

Q: need help understanding please help  Question 1 Find the volume of the solid obtained by rotating…

A:

Q: Find к for the space curve r(t) =2ti + (2a cosh (t/a))), a > 0. K(t)= (Type an exact answer, using…

A: Given:space curve- To find:

Q: can you solve this question for me please

A: The objective of this question is to determine whether each of the given integrals is proper,…

Q: Find the lim ex-y limit or (xy)-> (0,1) 2 cosx-1-y Show that it does not exist. DNES

A: To find the limit .To show that it does not exist.

Q: 1. f(x) = (4 — x²)5

A: Second derivative test for local maxima and minima :

Q: Page

A: The mean value of the probability density function 0  ≤ x ≤ 60 is simply the centroid's…

Q: Suppose that ƒ is a function given as f(x) = √−3x+5. Simplify the expression f(x + h). f(x + h) =…

A:

Q: Suppose that ƒ is a function given as f(x) = −x² + 5x − 3. Simplify the expression f(x + h). f(x+h)…

A: given function

Q: Complete the parametric equations of the line through the point (-6,1,-3) and perpendicular to the…

A: Point: (-6,1,-3)Plane: 6x-2y+2z=5

Q: 5 ст The slope of the tangent line to the curve y = at the point 8, is: x 8 The equation of this…

A:

Q: Suppose that f(x) = 16x6 In(x), x>0. (If an answer does not exist, enter DNE.) (a) Find all…

A: Note- As per company guidelines for a question posted we are allowed to solve first three sub parts…

Q: multiplicity. (b) Betermine whether the graph crosses or touches the x-axis at each x-intercept. (c)…

A:

Q: Suppose z = x² sin y, x = s² + 3t², y = 6st. Əz Əz A. Use the chain rule to find oz and 0 as…

A: Suppose .(A) By using chain rule to find  as functions of .(B) To find the numerical values of  when…

Q: 4) Graph one complete period of the function y = 3 tan (2x+)+ 1. Identify the period, phase shift…

A:

Q: Find the angle of intersection, in radians on the domain 0 <t≤, to two decimal places.

A:

Q: -olve 2 cos² (w) - 3 cos(w) + 1 = 0 for all solutions ≤w<2π พ

A: Explanation of the answer is as follows

Q: Given the points A: (2,3,-1) and B: (2,4,0), find the vector = AB

A: Given the points A:(2,3,−1) and B:(2,4,0).To find: the vector u→=AB→

Q: Use the formula for the sum of the first n integers to evaluate the sum given below. 3+ 6+ 9 + 12 +…

A:

Q: A. The instantaneous rate of change of demand with respect to price is _____when the price is ​$30?…

A: a) The instantaneous rate of change of demand with respect to price is called elasticity of demand.…

Q: horizontal asymtotes of 8x2+2x+1 2x2+3x−2

A: The objective of this question is to find the horizontal asymptotes of the given rational function.…

Q: Use only the properties of summation to evaluate the sum. Use the summation capabilities of a…

A: ∑i=116​(5i−4)= 616 (verified by wolfram alpha graphing utility) Explanation:To evaluate the sum…

Q: Use sigma notation to write the sum.

A: ​[2(1+n3​)2](n3​)+⋯+[2(1+n3n​)2](n3​)=i=1∑n​[2(1+n3i​)2](n3​)​Explanation:Step…

Q: Use the given information to find the exact function value. Simplify your answer as much as possible…

A: Given that the expression

Q: Suppose the Maclaurin series f(x) is f(x) = Σ Find the Maclaurin series for the following. f'(x) = Σ…

A:

Q: Let ā = - -71 – and 6 = −41 – 57. Find a. b -

A: Required answer is 33Explanation:

Q: Use a linear approximation (or differentials) to estimate the given number. e-0.01 Need Help? Master…

A: Given that  consider the function Linear approximation of f(x) about the point x=a is given by now,…

Q: Use the ratio test to decide if the series diverges. 1 converges or nen n=1 NOTE: Enter exact…

A: The serieshere needs to determine the series is converges or divergesuse the ratio testlet,  then

Q: Let s(t)= v(t) == 6+3 + 45t² + 108t be the equation of motion for a particle. Find a function for…

A: We need to find velocity and acceleration.

Q: 10) (a) Find the exact value of tan20 if tane = (b) Find the exact values of sinif cosa = -- 8 17 3…

A:

Q: Let a =. Find a unit vector in the direction of a

A:

Q: Find the length of the curve over the given interval. y = 10+10sinė, 0 ≤0≤2π Select one: ○ a. 20 O…

A: follow the solution part.Explanation:

Q: The region W lies between the spheres x² + y²+z2: 24 and ²+ y²+ z² == I' 16 and within the cone z =…

A:

Q: (b) Find parametric equations that represent the line segment from (-1, 7) to (1, 3) for 0 ≤t≤ 1.…

A:

Q: Find к for the space curve r(t)=(12 sin t) + (12 cost) j +9tk. K(t)=[ (Type an exact answer, using…

A:

Q: Question 4 Consider the curve 5x²+4xy+4y³ = 29125 (a) Show that P(-75,-5) is on the curve i.e., show…

A:

Q: Let a = . Find a unit vector in the direction of a

A: Unit vector in direction of a isa^= &lt;45​2​,45​−4​,45​−5​&gt;Explanation:Given:a=&lt;2,−4,−5&gt;…

Q: [ (sec y) (tan y (sec y)(tan y - sec y) dy

A: (secsecse  se secCWhere , C is constant of integration.

Q: Please don't provide handwritten solution...

A: The objective of this problem is to find the rate at which water is being pumped into the tank. We…