Find an equation of the tangent line to the curve at the given point. y (4,16) (Express numbers in exact form. Use symbolic notation and fractions where needed. Let y = f(x) and give the equation in terms of y and x.) equation of the tangent line:

Q: A) estimate the area of the graph of f(x) = 25 - x² From x=0 to x=5 using approximating rectangles…

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Q: Lim x tends to pi/4- (LHL) √(1-√sin2x)/(pi - 4x)

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Q: Find the vector, not with determinants, but by using properties of cross products. (j - k) x (k - i)

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Q: 5 If [ f(x) dx = 18, then 5 (f(x) + 4) dx is equal to:

A: Using the properties of Integrals

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A: We have given two curve in above problem. We have to find area between them

Q: Hos solv the step? 0.10.9062cos (1-√√/3x) d x [sin (1. (3x) 3 sin (1-√√3a) - sin (1-√3(-0.1)) sin…

A: To find the given step how to came from the above step

Q: Find the distance from the point (3,-7,-1) to the plane -x + 5y + 2z = 34.

A: Here is the solution:

Q: 3+2=?

A: What is the value of 3+2

Q: Use the Limit Comparison Test to determine if the series converges. k³ +7 k(k+ 3) (k − 2) (k+1) k=1…

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Q: Hos solv the step? ₁0.9062cos (1-√3x) d x [sin (1-√√3x) -√√3 √³x)] -0.1 -0.1 sin (1-√√3a) - sin…

A: We have to solve the step  sin(1-√3a)= -0.9556+0.9210

Q: a) Find a and c so that (a, 1, c) is a point on the line through (0, 2, 3) and Justify your answer.…

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Q: Find the indefinite integral using the substitution x = √x√4 + x² dx + C 2 tan(0)

A: SOLUTION-

Q: Solve the given differential equation by separation of variables. e-y + e-5x - y exy dy dx

A: To find the solution of D.E.

Q: Let à = i-5j - 2k. Find |āl.

A: Using the formula if  a→= x i^ +yj^ +zk^then a→=x2+y2+z2

Q: ·S In (x) vxln(x)-x X dx

A: We know that integration power rule is - Integration of xn is xn+1/n+1 + C . Here C is integration…

Q: The angle between the two vectors is not equal to Select one: O True O False u= and v= 0= π

A: Here we use the concept of dot product of the vectors.

Q: Choose the correct option. a) Which of the following is not a perfect cube? i. 512 iii. 216 ii.…

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Q: What two positive real numbers whose product is 19have the smallest possible​ sum?

A: We want to find the two positive real numbers whose product is 19 and the smallest possible sum.

Q: Using implicit differentiation, find dy dx √xy = − 1 + xy

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Q: CONVERSATION/OBSERVATION Understanding Types Of Graphs 1. Imagine you were given three different…

A: According to the company rule, we can answer only first question and rest can be reposted.

Q: 1. If y = sin x² x =²), ex find dy dx

A: Given y=sinx2-xex To find dydx

Q: Choose x such that the following two vectors are parallel u= and v= O -7 O None of the others 07 O…

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Q: (A) 3y²ex+y²dx (B) 3) [3y²e²+ y² dx 0

A: In both integration we have to integrate with respect to x . So we treat y as a constant & solve…

Q: Given the conic section = Intercept(s): Focus (foci): 1 5+7 sin(0)' find the x and y intercept(s)…

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Q: S In (x) √xln(x)-x =dx

A: Please see the below picture for detailed solution.

Q: Evaluate the following integral using inversion of order: SS²x5 dydx

A: I =∫xn dx= xn+1n+1 Ans = 1/72

Q: b. The formula A(t) = 19.6e0.0138 models the population, A(t), of a US state in millions, t years…

A: Given: At=19.6e0.0138twhere At denotes the population in a US state in millions, t years afterthe…

Q: The length of the curve r = sin² for the period 0 ≤ 0 ≤ π is 2 6 2 O 8 O 4 O None of them O

A: The objective of the question is determine the length of the curve given in polar form.

Q: B-Find the area of the region inside the curve 1+cos@ and outside the curve -1 and graph the two…

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Q: A-Show if the series is convergent or divergent (2n)! 2n n²

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Q: Given the equation of the curve y = 0.1(1600-x²). Find the area bounded by the curve and the x-axis.…

A: Note: Since you have posted multiple questions we will solve the first question for you. If you want…

Q: Using Linear Equation, find a general solution of: dy x x - y - 5x4 3x² + 2x = 0 dx

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Q: sinx13 cOSX on the interval [0, π] Average value=

A: According to the company rule we can answer the first question and rest can be reposted.

Q: 7. Tammy is golfing. She wants to drive her ball from the tee to the hole that lies due east.…

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Q: ·S In (x) √xln(x)-x =dx

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Q: Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve…

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Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

A: Basic partial derivation is used.

Q: Let a be a real number. Evaluate the following integral: So fx + y dxdy

A: We have to evaluate the integral ∫0a∫y-1y+1 x+y dx dy  where a is a real number.

Q: mx + + 1) (x+1)^ then value of m +n is (where n is a prime number) X-2 dx equals ex + C

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Q: The Cartesian equation equivalent of polar equation r = 4tane sece is y True False O

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Q: Solve the given initial-value problem. The DE is homogeneous. 3 xy² dy = y³ y -x - x³, y(1) = 3

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Q: If A is square matrix of order 3 such that|3 A| = 54. Find |A|

A: Using the properties of determinants

Q: Given u x 7 = (-1,4, -2), find ( − 3v) × (u + 5v).

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Q: A triangle is placed in a semicircle with a radius of 6ft, as shown below. Find the area of the…

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Q: The area enclosed by one petal of the polar curve r = cos20 is False True O

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Q: Define R as the region that is bounded by the graph of the function f(x) = -2e, the x-axis, x = 0,…

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Q: - If f(x, y) = cos(2x) − x² e5y + 3y², then fxy = -10x e5y True O False O

A: A detailed solution is given below.

Q: 6. Which substitution can work to compute for the indefinite integral fx√√x + 5dx? A. u=x C. u=x+5…

A: we use substitution method to  find the value of integral

Q: Drag and drop your answer into the box: (a) An antidervative of f(x) is (b) The indefinite integral…

A: Solving the question by finding the value of the problem.

Q: Differentiate ex with respect to x, assuming that y is implicitly a function of x.

A: Here we have to use the concept of implicit derivative