Evaluate the definite integral. NOTE: Enter the exact answer. L²||ti ti = + t²i||dt

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Q: Assume f(x) is a differentiable function such taht f(1) = 3, f'(0) = 2, and f'(-2) = 7. Evaluate the…

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Q: Find exactly T(t) and N(t) for x = e'cost, y = e'sint, z = e' for t= 0. [Choose the correct answer.]…

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Q: 5. What is the derivative of the given function below? * x² + y² = xy dy dy dx dx Option, dy dx = =…

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Q: Find a power series solution of the differential equation y' = 4y

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Q: Question 5 > The plot below represents the function f(x): 3 3-4-32 1 2 3 4 Evaluate f(-3): f(-3) -…

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Q: Q2: find dw/dt at given value point for the following function

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Q: 7(e)₁² X y= » - [1-171² 2 sec- y = (tan 17 1² ² X y = [cscx]arcsin (cos.x)

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Q: Calculate the line integral [(of).do where f(x, y, z) = x ² ¹² + 4 xy² z yz с + е хуча and C is the…

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Q: N) dy x dx X (1+y) y (1-x)

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Q: Solve for 0 <0 < 2π Separate your answers with commas. 0= sin 40+ sin 50 = 0.

A: Here, the given equation is: sin 4θ+sin 5θ=0...(1)

Q: Exponential function Copy the table onto your paper, and fill in the y-values for y = 3*. X y 0 1…

A: Since, you have posted multiple questions. As per guidelines, we"ll solve only first question. If…

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Q: I need help on number 12. Thanks!

A: 12. The given differential equation is y'-y=0  .................................. (1) We assume the…

Q: 2x²+x-1 Evaluate -dx using method of partial fractions. Which of the (x-1) (x³+1) following is the…

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Q: Which of the following is correct? 1. cosh²x + sinh²x = 1. II. sinh x cosh y = sinh (x + y) + sinh…

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Q: Mode QuesX 4) Cor + (y + 5)² + (y + 5)²

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Q: ƒ dx = f(+ g(x)) dx, then A + f g(x) dx is equal to x³+x A. -1 B. -1 + In(5/2) C. 1 D. -1 + In(7)

A: Given that,

Q: Find the critical point of the function, then determine if it is a local maximum, local minimum, or…

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Q: Question 5 Given the function: 5x 6 x < 0 ƒ(z) = { 5x 12 x 20 Calculate the following values: f(-1)…

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Q: f(x, y) = 3x² - y x4 x² + 2y ² 1 (x, y) = (0,0) 2 D (X,Y)= (0,0) 1 Determine if f is continuous at…

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Q: d'y Given: y = ax + bx³ + cx² + dx + e, where a, b, c, d, e are constant, find dx5

A: Topic:- derivatives

Q: 6. 15 4 3 5 1 23 24 -3 -6-5-43-2 2 3 4 5 6 -6 Write the domain of the function using interval…

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

Q: Round your answer to four decimal places, if necessary. Approximate the area under the curve on the…

A: We have to find the area by right endpoint rule.

Q: The area of a triangle with sides of lengths a and b 1 and contained angle is A = a b sin 0. If a=2…

A: Use the application of derivative to find the rate of change.

Q: Using integration by parts, Then k is? (a) - 1.5136 ²x³ cos x³ cos(x²) dx = k - [*x sin(x²) dx 0…

A: Solve it

Q: Describe the graph of the equation. r = 5 cos ti - 8 sin tj+ k O An ellipse in the plane z = 1,…

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Q: Find the integral: x2-2/x+1 dx choices: a) x2/2 - x - In(x+1) + C b) x2 - x - In(x+1) + C c) x2…

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Q: lim- LIMIT VALUE: z²-16

A: As per guidelines if multiple questions are posted we are allowed to solve only 1st question..…

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A: Given: The open rectangular box of maximum volume that can be made from a sheet of carboard 21 in by…

Q: Use the second derivative test to find the location of all local extrema in the interval G for the…

A: Given f(x)= -2ex/(-4x-1)= 2ex/(4x+1) So, f'(x)= [2ex(4x+1)-8ex]/(4x+1)2 To get local extrema we put…

Q: The shaded region between the graphs of y = 2x² + 20 and y = 3x - 15 is displayed below in orange.…

A: Area bounded by the curves : If f(x) and g(x) be two continuous function and f(x)≥ g(x) on a,b ,…

Q: What is the slope of the tangent line at (0,3) to the function f(x) = -sinx+3

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Q: Calculate the derivative. f(x) = (6ex - 7x²) (x³ + 1) (Use symbolic notation and fractions where…

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Q: 3) f(x, y, z) = x² + y² -2=²+ = ln(x), (1,1,1)

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

Q: The series ∞ (-10) k k! k=1 is an alternating series but we can apply the ratio test to ∞ (-10) k k!…

A: We have to check convergence of series with the help of ratio test.

Q: A function f(x) is said to be continuous at x = c if the following three conditions are satisfied:…

A: Solution is here

Q: 1. Use the graph of y = f(x) given below to find the answer to each of the following. You do not…

A: By using the graph of y=fx given below to lisy all the intervals on which f is increasing.

Q: Given the function of f(x) = 8x² - 8x on the interval [0, 1], find a point c between 0 and 1 so that…

A: Answer is in step 2.

Q: Find the equation of the line tangent to the graph of f(x) = (In x)5 at x = 2 MECHI y=0 (Type your…

A: Use derivative for finding the equation of line .

Q: dx x² - 2x - 4 sec 0 csc 0 S integrand is? (a) (c) √5 is solved by trigonometric substitution, the…

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Q: Solve the optimization problem. F = Minimize F = 11x² + 11y² with xy² = 16.

A: Given problem:- Solve the optimization problem.   Minimize F = 11x2 + 11y2 with xy2 = 16

Q: Calculate the derivative. y = x4 - 4 x² 5 (Give an exact answer. Use symbolic notation and fractions…

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Q: Suppose f, g have the following values: f(3) = e5 and g(3) = 2. ƒ'(3) 10 and g' (3) = = 8. 4 Let y¹…

A: To find the value of y' at (3,-3).

Q: S sin (Inx) dx? How many times will you perform integration by parts to evaluate

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Q: Use a sum or difference formula to find the exact value of the following. sin 148° cos 103° - cos…

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Q: Write the equation of a sine or cosine function to describe the graph. MA

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Q: Use the Law of Sines to solve for all possible triangles that satisfy the given conditions: a = 30,…

A: I am attaching image so that you understand each and every step.

Q: Which value of az is NOT in the domain of the function G(z) - = 28 12-25 -?

A: Use the definition of domain  to find the value of x

Q: 82. lim (1 + 10)²

A: Explanation of the answer is as follows