Find the derivative of the following function. Factor and simplify so that no negative or fractional exponents appear in your final answer. f(x) = (2x² + 5)³ (4x³ - 7)²

Q: Consider the piecewise defined function shown below. Assume m is a constant and m + 0. Note: Use…

A:

Q: 1. The value of limx→0+ √√x ln x A. 00 B. -∞o C. 0 D. -1 E. 1 F. None of these

A:

Q: 4 M t 1 C- ts- 2- 1- o 14 T . E- T о O f(x)=-=(x-2)²-2

A: Given query is to find the graph of the function.

Q: Find u and v if u+3v = 3i − k and 6u − v = i +j+ k.

A:

Q: The demand curve for original Iguanawoman comics is given by (357-p)2 (0 sps 357), 100 where q is…

A:

Q: Q1. Compute the following derivatives: = (a) dx (c) (b) =[5 - 3x] = = dx [] = d) [6 = dx

A: see below the answer and calculation

Q: Let p(x) = x³ - 17x² + 11x + 76. Compute p '(x) and use it to find all values of x for which p '(x)…

A:

Q: question is not answered

A:

Q: Consider the graph of y = f(x), shown below. 5 4 3 2 1 ਆਪਣੀ -3 -2 -1 1 2 3 14 5 -2 -3 -4 W The…

A: Given graph:-

Q: Let (-1)n-1un be an alternating series. The Alternating Series Test (AST) has 3 conditions to check…

A: The given series ∑-1n-1un be an alternating series. We have to find the conditions for the…

Q: Please help solve this and explain for me. Thank you. The temperature at point (x,y,z) in space…

A:

Q: (See image. I only need question C answered, thanks!) A ball is dropped from a height of 8 feet and…

A: Solution to part c is added below as asked by the student.

Q: Which of the following properties describe the sequence {} O O O Not bounded and not monotonic…

A:

Q: Prove by strong induction that root of 2 is irrational.

A:

Q: At what point on the curve y = 8 + 2ex - 4x is the tangent line parallel to the line 4x - y = 1? (x,…

A:

Q: Find exactly the vector oppositely directed to v = (3) and half the length of V. i i

A:

Q: Find the derivative of the given function. Use all lower case letters. ax² + b C h'(x) = h(x) =

A:

Q: Let f(x) = ln(3x + 5). Show by induction that the nth derivative of f is given    by…

A:

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A:

Q: Each function below describes how something changes. Use the description to determine which…

A:

Q: Population Movement In 2008 the population of a country, broken down by regions, was 54.6 million in…

A: Let the 2008 population figures be represented by 1×4 matrix AA=54.665.6112.670.5   Let the…

Q: For the function f(x)=3x³ - 2x²+2x+8, find f'(x). Then find f''(0) and f''(5). f''(x) = 0 www

A:

Q: Differentiate the function using one or more of the differentiation rules. y: 1 = (3 + 2x5) 5 y' =

A: We know that, The SUM/Difference Rule: f±g'=f'±g' The Power Rule: ddxxn=nxn-1 The Chain Rule:…

Q: The function f(x) has tangent line equation y = 4(x-a)-6 at x = a. Both are shown in the graph…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) [₂2/01L 81 + ex dx

A:

Q: A function f(x) and interval [a, b] are given. Check if the Mean Value Theorem can be applied to f…

A: As per Mean Value Theorem f'(c)=f(b)-f(a)b-a          Equation 1

Q: 1-47 Evaluate the integral. 1. fsin'x cos³x dx 2.

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find the norm of v. NOTE: Enter the exact answers. (a) v = (3,-3) ||v|| : = (b) v = −7i+j ||v|| : =…

A: As we know that, If the given vector is v=xi+yj+zk or x, y, z then the expression for the norm of…

Q: 5. Using integration by parts once, the integral (In x)2023 dx becomes (In x)2022 A. 2023 + C x B.…

A: Note that, according to Bartleby guidelines, we can answer only the first question in the case of…

Q: Find the inverse. 1 -8 2 -1/10. 71 10 10 2 -8 -2 ;]

A:

Q: For the function graphed in the figure, are the following nonzero quantities positive or negative? 2…

A:

Q: The graph of a function f and a tangent line to f at the point B are shown in the figure below.…

A: Given: The graph of a function f and a tangent line to f at point B are shown in the figure below.

Q: Find the vertex of: f(x) = (x − 2)² – 1 - The vertex is

A:

Q: log 457,129 is between log 457,129 A and

A: As per our guidelines, we only solve one question and rest of the question will be reposted. Formula…

Q: True or false: If the absolute maximum value of f(x) on a closed interval is f(a), then it is…

A: Please see the below answer.

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

A: Solving the following problem

Q: 3. [ substitution ] Evaluate the integral using 2 sin x method S (2+ cos x)² da

A: L=∫2sinx(2+cosx)7dx∫xndx=xn+1n+1+c

Q: Find x²√√x² + 16 Solution Let x = 4 tan(0), (1 √x² + 16 = √16 (tan² (0) + 1) = √ 16 sec²(0) =…

A:

Q: A beverage company manufactures 2-liter pineapple juice to be packaged in cylindrical cans made of…

A: Given :The surface area of this cylinder = 2πrr+hV=πr2h

Q: If f and g are two functions that are differentiable at every x in an interval (a, b), and if ƒ'(x)…

A:

Q: Use the graph of f" shown below and the letters A, B, C, and D representing x values to answer the…

A:

Q: A car rental agency rents 420 cars per day at a rate of $30 per day. For each $1 increase in rate,…

A:

Q: Determine if the following statements are true or false. (a) If a function is differentiable, then…

A: Given query is to find the statement i true or false

Q: Given f(x) = 2x³ + 12x² + 6x + 13 3 The critical values of f"(x) are x = Concave Down interval is O…

A:

Q: Angle a lies in quadrant II, and tan a = What is the exact value of sin (a + B)? Enter your answer…

A:

Q: 7. Find all local and global maxima and minima of the function f(x) =2x^3 − 3x + 2 in the interval…

A: To find all local and global maxima and minima of the function fx=2x3-3x+2  in the interval -1, 2.

Q: Use the following piecewise defined function to answer the questions. from the definition.) = {x₁ [x…

A:

Q: Find 1 x²√x² + 16 J Solution Let x = 4 tan(0), - Thus, we have sec(0) tan²(0) dx. -<6 2 = << . Then…

A: According to question,Given Integral,∫1x2x2+16dx

Q: Find the limit by rewriting the fraction first. lim (x,y) →(1,6) X#1 xy-y-4x+4 X-1

A: To find the limit by rewriting the fraction first. limx, y→1, 6 xy-y-4x+4x-1 where, x≠1

Q: Biologists have proposed a cubic polynomial to model the length L of rock bass at age A: L =…

A: