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Q: evaluate the limit.

A: To find the limit

Q: evaluate the limit.

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Q: What is the slope of the line y = −4x − 9?

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Q: Find the dimensions of the rectangle of maximum area that can be inscribed in a circle of radius r =...

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Q: 60. Consider the region bounded by the graphs of y = Vx tan and y = 0 for 0 < x < 1. Find the volume...

A: We have to use Disk method to find the volume with radius = y= sqrt(x*tan^-1x) x is from 0 to 1. ...

Q: 25. Let f(x) be a continuous function. Express + ()] lim п—оо as a definite integral.

A: Definite integral in the form of the limit of the Riemann sum: Let f(x) is a continuous function o...

Q: Use Leibniz's Rule to find the derivatives of the functions in Exercises 31–-38. sin x 32. f(x) = 31...

A: Hey, since there are multiple questions posted, we will answer first question. If you want any speci...

Q: find the transition points, intervals of increase/decrease, concavity, and asymptotic behavior. Then...

A: Find the derivative of the function,

Q: Find the maximum of y = xa − xb on [0, 1], where 0 < a < b. In particular, find the maximum of...

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Q: 2.) (3x + x2) sin(2x) dx Use whatever method you want to

A: Part 1

Q: Determine the dimensions of the rectangle of largest area that can be inscribed in the right triangl...

A: Given the figure:

Q: Fermat’s Theorem does not claim that if f'(c) = 0, then f (c) is a local extreme value (this is fals...

A: The given statement is “Fermat’s Theorem does not claim that if f'(c) = 0, then f (c) is a local ext...

Q: In Exercises 13–24, find the derivative of y with respect to the appro- priate variable. 1 14. y = s...

A: Hello thank you for the question. As per our guidelines we are allowed to answer one question. So, w...

Q: Kicking a field goal An American football player wants to kick a field goal with the ball being on a...

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Q: 31. Take any map and draw a circle on it anywhere (Figure 6). Prove that at any moment in time there...

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Q: Use the theorems on derivatives to find the derivative of the following function: ((x3 + 2x2 + 4x + ...

A: Consider the function

Q: A max-min problem with a variable answer Sometimes the solution of a max-min problem depends on the ...

A: The radius of the right circular cone is R and the height of the right circular cone is H. The cross...

Q: The integrals in Exercises out using tables. converge. Evaluate the integrals with- dx dx x.001 1. 2...

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any s...

Q: Consider the function h(x), for whichh(5)=11 and h′(5)=−5. Find f′(5) for the function f(x)=h(x)/x

A: Given function is Differentiating both sides with respect to x using quotient rule of differentiati...

Q: Find the indefinite integrals (most general antiderivatives) in Exercises You may need to try a solu...

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Q: evaluate the limit.

A: Given:

Q: What are the domain and range of f (x) = ln x?

A: Given function: Domain: The domain of a function is the set of input values for which the funct...

Q: Suppose that f(x) dx = 5. Find V3fә de f(u) du b. a. [-f(x) ] dx c. f(t) dt d.

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Q: | (sin x)/x, 0 < x< l1, 13. Let f(x) = x = 0 a. Show that xf(x) = sin x, 0 < x< . b. Find the volume...

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Q: 1/10 1.A) e* cos(5x) dx integration by parts

A: Here we have to do integration by parts: Apply integration by parts u as e3x and v = cos5x

Q: Higher-Order Derivatives f(x)=2x^4-3x^3+2x^2+x+4 find f^4(x) =

A: Let the given function is f(x) = 2x4 -3x3 +2x2 + x + 4. Now we have to find the fourth derivative...

Q: 38. Semicircular plate Calculate the fluid force on one side of a semicircular plate of radius 5 ft ...

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Q: Please answer part d

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Q: When is ln x negative?

A: When is ln x negative?

Q: find a point c satisfying the conclusion of the MVT for the given function and interval. Then draw t...

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Q: verify Rolle’s Theorem for the given interval by checking f (a) = f (b) and then finding a value c i...

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Q: Find the region bounded by y = x^2 +1, y = 10, x = 0 (in quadrant 1). For the following volume probl...

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Q: There is multiple questions

A: The surface area obtained by rotating the curve x=g(y), a<y<b about y axis is given by Rew...

Q: True or False? If f (c) is a local min, then f'' (c) must be positive

A: If f (c) is a local min, then f'' (c) must be positive. We will disprove this with the counterexampl...

Q: For this problem, we want to integrate f (x) = (x − 2)/(x^2 + 4). 5c please!

A: To integrate the below function by splitting the integral into two integrals. Split the integral of...

Q: Find the region bounded by y = x^2 +1, y = 10, x = 0 (in quadrant 1). For the following volume probl...

A:

Q: Determine where f (x) = (1,000 − x)2 + x2 is decreasing. Use this to decide which is larger: 800^2 +...

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Q: ) Find the area bounded by Y,=cos(x) Y,= sin(x) X-0 and X-IT/2 graph it and show

A: Find the point of intersection of 2 curves.

Q: 30. log, (2) vs. log, (x) g(x) = log2(x)? Here is one way to find out. a. Use the equation log,b = (...

A: a) We use to express f(x) and g(x)

Q: determine whether or not the IVT applies to show that the given function takes on all values between...

A: The given function is

Q: 8. Order the following functions from slowest growing to fastest growing as x→∞. a. 2* c. (In2)* b. ...

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Q: y=(sinx)x d2y/dx2 ?

A: Apply exponent rule and solve:

Q: Let f (x) = x5 + x2. The secant line between x = 0 and x = 1 has slope 2 (check this), so by the MVT...

A: We plot f(x) and the secant line between x = 0 and x = 1 using a graphing calculator.

Q: 53. Use the substitution u = x + 1 to evaluate the integral I dr.

A: Differentiate u with respect to x, du= 4x3 dx du/4x3= dx

Q: 42. Whatever the value of p > 0 in the equation y = x²/(4p), the y-coordinate of the centroid of the...

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Q: In which quadrant do the following points lie?(a) (1, 4) (b) (−3, 2) (c) (4,−3) (d) (...

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Q: find (x² – 2x + 1)e²* dx dx 9. 10. fun tan - y dy y dy 11. 12. sin- x sec² x dx 4x sec2 2x dx 13. 14...

A: Hello thank you for the question. We’ll answer the first question since the exact one wasn’t specifi...

Q: What is the fourth derivative? x^12+1

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Q: The indefinite integral dæ can be solved using either of the three methods: 1. integration by 4+2? s...

A: In the first step we do integration by substitution: According to the question, lets substitute u ...

Q: sketch the graph of a function f satisfying all of the given conditions. (i) f' (x) > 0 for all x...

A: The graph of a function f satisfying all of the given conditions. (i) f' (x) > 0 for all x, and(i...

Transcribed Image Text

Find the derivative of f (x) 32 2x+3 Enclose numerators and denominators in parentheses. For example, (a – b)/ (1+n). Include a multiplication sign between symbols. For example, a · T. f' (x) =