10 Find an equation for the tangent line to the graph of y = (x³ - 25x) ¹0 at the point (-5,0). The equation of the tangent line is y= (Simplify your answer.)

Q: zl 5. Trigonometric form of the quotient of = 6cis (2); z2 = 2cis () is:

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Q: Find the transition points. y = 3x² - 42x6 (Use symbolic notation and fractions where needed. Give…

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Q: 3- Find the length of the curves in Exercises 1-4. X = (y3/2/3) - y¹/2 from y = 1 to y = 9

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Q: If f is continuous on [a,b], and f(x) > 0 then (A) True B) False √√° √F(x) dx = ₁ √ [F(₂ a - f(x) dx

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Q: Let c be a constant, and let h(x) = sin-¹ (cecx + x). Find h'(x). h'(x) c²eca + c 1-c²e2cx 2cxeca…

A: Solution is done in step 2

Q: 5. Solve the equation = 170. 6. Solve the following logarithmic equations. (a) log, (+5) = log, 3…

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A: Given problem:- cos2(x) sin(x) dy+(ycos3(x) -2) dx=0

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Q: Atmospheric pressure P in pounds per square inch is represented by the formula P = 14.7e-0.21x,…

A: Given :Atmospheric pressure : P=14.7 e-0.21xx= number of miles above sea level

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A: Triangle law

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Q: Please kindly show all working. Thnx. 1) Let f(x)=x3−3x2−9x+25. Use the derivative…

A: Given function,f(x)=x3−3x2−9x+25.We know that.Suppose that x=c is a critical point of fx then, If f…

Q: Find the instantaneous rate of change for the function at the given value. f(x) = x² + 3x at x = 0…

A: We can find the instantaneous rate of change as below

Q: f2₁ (4x + 5) dx

A: ∫-12 4x+5dx

Q: Suppose that f(x) = 5x6 - 7x5. (A) Find all critical numbers of f. If there are no critical numbers,…

A: We have to solve given Questions.

Q: In t years, the population of a certain city grows from 500,000 to a size P given by P(t) = 500,000…

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

Q: 1. x Cos² y dx + tan y dy = 0 2.2 x yy' = 1 + y² @ a given condition x = 2, y = 3

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Q: f(1 ¹ (1 + 2/1/2) ² du u²

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Q: 3. Let there be some a, b ER such that f(a)f'(a) = f(b) f'(b) + 1. Show that f f(x)f"(x)dx ≤ 1.

A: This is a problem related to integration. Based on the general formula and concept we will prove the…

Q: followin COSX 3. f- dx 1+sinx 4. f (sinx + cos x)² dx 203 (y² +1) 20 dy 5. f

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Q: Find lim [x csc(x)] as x approaches zero.

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Q: The proper way to evaluate f(x + h) for the function f(x) = 3x²-x+4 is f(x + h) = 3(x+h)² - x +h+4…

A: Topic:- function

Q: 2. 8 2 + (-1) 5+

A: Here we have ∑k=1∞2+(-1)k5k

Q: 3. The small circle is tangent internally at (-2, 0) to a big circle. See the figure below Find the…

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Q: 3. y²(x + 2y) = 8

A: The Solution is dydx=-y2(x+3y)

Q: Consider the matrices shown below: A Find the value of K such that det (BT) 64 - 1 с 3K and AT is…

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Q: Show that f Va²-t²dt = a² sin-¹(2) + x√a²-x².

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Q: The graph of a function y = f (x) is shown below. Use the graph to estimate all (there may be more…

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Q: 1. what is the basic concept of a vector? How is this vector calculated? What techniques s/rules can…

A: A vector is a quantity which have direction as well as magnitude.

Q: S 2+2 cot (2²+42 - 3) -dz

A: Solution of given question is written in below steps.

Q: S tan-1 е' 1+4t² 2t dt

A:

Q: S 0 Question 8 A lighthouse L is located on a small island 2 km from the nearest point A on a long…

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Q: SUBJECT

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Q: Assume y = f(x) is a function that is continuous on the real line. Which of the following statement…

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Q: dz dw || Z-W z+w

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Q: 2. √√√x + y + xy = 21

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Q: Find the standard form of the equation of the circle whose diameter is the line segment joining (-2,…

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Q: Find the first three terms of Maclaurin series for F(x) = In (x+3)(x+3)²

A: A Maclaurin series is a special case of a Taylor series, obtained by putting x = 0 i.e.,

Q: (a) f dx 2 √3x-x²

A: Solution of the problem as follows

Q: Given than [(x) f(x) dx = 7 and f (x) da = -5, which of the following is NOT TRUE 6 ® [f(x) dx =…

A: Given that ∫-23fx dx=7 and ∫36fx dx=-5, then to determine which of the following is not True.A…

Q: Find the absolute maxima and minima of the function on the given domain. T(x,y) = x² + xy + y² - 9x…

A: Given :T(x,y)=x2+xy+y2-9x+3

Q: 9. (20 pts) Find the area between (bounded) by the curves y = x² + 10x and y=2x+9.

A: Given: curves y=x^2+10x , y=2x+9 We have to find the area between the curves

Q: Consider the function f(x) = 2x + 1. Find its derivative

A: The limit definition of derivative is: For a function f(x), the  derivative of f(x) is defined as:…

Q: 5. 2 Let f(x) = 5x4. +8√x - 3. x² (a) Find f'(x). (b) Find an equation for the tangent line to the…

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Q: Q3/ Evaluate four of the following integrals. ( x³+1 sinx cosx dx b. f*+¹ dx c a. S √1+cos2x x²

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Q: Determine if the function is continuous at a given value of x. Show your complete solution.

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Q: y = ln 1-x² 1+x²

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Q: Which of the following is NOT true about the curve * y = x3 – 5x2 + 2x+8? (-1,0), (2,0) and (4,0)…

A: The given function is: y2=x3-5x2+2x+8y=±x3-5x2+2x+8 If a function is symmetric with respect to the…

Q: In 2000, the population of a city was 154,800. The population had dropped to 112,700 by 2007. Find a…

A: We have to find the formula for A(t).

Q: 5) Find the area enclosed by one petal of r= cos (40)

A: