7.(a) f(x) tan (In x) + 52 7.(b) f(x) = log2 (tan r) + In (¹)

Q: Question 7 Find the partial derivative of z with respect to x 8: da = -2x (3x²+1) sin(x²) + 6xcos…

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Q: ( (tano-1)² do

A: Given ∫[tanθ-1]2 dθTo evaluate the integral:

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Q: Question 1. A critical point of the function g(x, y) = ex y + 3x²y-y is (0,0). Use the Second…

A: Explained below

Q: Prove the limit below exists, by using the Binomial Theorem and the Monotone converge ONLY. Do not…

A: Prove the limit below exists, by using the Binomial Theorem and the Monotone converge ONLY. Do not…

Q: 4. For the series Σ=1+()", does it converge and if so what does it converge to? * n²

A: We have to check that series 1/2*(2/5)n  where n=1 to infinity. Is convergent or divergent.

Q: Consider the graph of y = f(x) shown below in blue. Find the open interval(s) where f'(x) is…

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Q: Assume that the random variable X is normally distributed, with mean μ = 70 and standard deviation…

A: To find the probablity P(X>a)  then we have to convert the expression into  Z-score value of the…

Q: Find the local maximum and minimum values and saddle point(s) of the function. If you have…

A: We will use calculus of two variables to find the required information about the function.

Q: Find the derivative using logarithmic differentiation. r³(2x - 1) (5x + 1)7(x + 1) 14. y=

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Q: Given the functions: f(x)=x²³-8x g(x) = √2x h(x) = 6x+7 Evaluate the function h (f(x)) for x = 3.…

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Q: c. Given f(x) = 2x - 3, g(x) = -4x² + 9, h(x) = 4x² - 12x +9; find 1. f(x)* g(x) 2. h(x)/ f(x) 3.…

A: solve

Q: Ju 2²u Consider the heat equation = Ət for a bar of length L=1, with non homogeneous boundary…

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Q: -1.5 -4.5 -1.5 Let [ f(x)dx = 5, |_^*^* f(x)dx = 6, [*¹*³ f(x)dx = 5. -6 -6 Find and -3 [²₁ f(x) dx…

A: This question is related to definite integration, we will solve it using given information.

Q: Evaluate the following antiderivatives. S 4x dx 4e e8x +4

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Q: hid. The line y d. The line y = -5/8 -5/8 redbuthents 2 y 0 X = ochiul 14 4 X = - y² 2 1 y² dibel 2…

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Q: Question 10 Given z = (e-22) (sin y), find 92 O-2e-2 O-2 e 2 (sin y) + e-2 (cos y) O-2e-2 (sin y) -2…

A: We have to find derivative of given term.

Q: S x² e¹x dx

A: EVALUATE USING INTEGRATION BY PARTS  For the function x2e4x .

Q: If we know that g is a derivable function such that g'(81) = 6 and f is a function given by f(x) =…

A: Given :f(x)=gx4g'(81)=6

Q: a. Set up an integral for the length of the curve. b. Graph the curve to see what it looks like. c.…

A: Explanation of the answer is as follows

Q: Find the directional derivative of f(x, y) = x² - 2xy at the point (1, -2) in the direction from…

A: directional derivatives

Q: Two matrices A and B are multiplied to get AB if O both are rectangular both have same order number…

A: If A and B are two matrix then matrix AB is defined only when  (A) A and B are of same order (B) The…

Q: Find the general solution of the given second-order differential equation. 30y" 19y' 5y = 0 -…

A: See the details solution in below

Q: Evaluate the following antiderivatives. S dx √x²+2x+5

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Q: Find the volume of the prism. 12 ft 27 2 ft 3/ ft V = [?] ft³ Write your answer as a mixed number…

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Q: What is the area of the region bounded above by y = -3 MX. 54-3-2-1 1 2 3 4 45 O ভাল লাল নাল O O O…

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Q: Solve. |x-8=24 Select the correct choice below and, if necessary, fill in the answer box to complete…

A: option (A)  is correct. see below the calculation

Q: Solve for m ffm m(8xy + x?)dxdy =3, 0<y<x<1

A: we can solve as follows

Q: 59. x² + 2x + 4y - 3 = 0

A: Here we have to find the vertex and focus of parabola.

Q: Find the average value of f(x) = x² on the interval [2, 4]. Answer:

A:

Q: Write and evaluate the definite integral that represents the area of the surface generated by…

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Q: Find all critical numbers for the function. State whether it leads to a local maximum, a local…

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Q: A particle moves in the yz-plane along the curve represented by the vector-valued function r(t) = (4…

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Q: Consider the integral 11 [™ (22² + 2x + 1) da (a) Find the Riemann sum for this integral using right…

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Q: Calculate the future value of end- of-month payments of $500 made for 4 years into an investment…

A:

Q: ƒ (t) = -{ 5,03

A: We know the followingLf(t)=∫0∞e-stf(t)dtLeat=1s-aLtn=n!sn+1Lsinat=as2+a2Lcosbt=ss2+b2

Q: X f(x) g(x) -2 5 1 -1 2 3 0 4 1 -2 2 -4 -3 -6 -1 f'(x) -4 -2 1 5 -5 g'(x) -1 3 -3 4 2

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Q: Asymptotic to x= 0, x=5 and y=0

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Q: Question 4. Determine if the series Σ n=1 5n+1 7-2 converges or diverges. If the series converges,…

A: We have to find the given series is convergent or divergent  , if the series is convergent give its…

Q: A region bounded by f(y) = √√√y, y = 4, and x = 0 is shown. What is the volume of the solid formed…

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Q: Use the properties of the definite integral to express the definite integral of ƒ (x) = 6x³ − 4x² +…

A: Given :f(x)=6x3-4x2+2x-3interval [ 1, 3 ]

Q: a. Find a curve with a positive derivative through the point (1, 1) whose length integral (Equation…

A: To find curve satisfying the given conditions.

Q: For the function f(x) = 2x2 - 5x a) Find f'(x) from FIRST PRINCIPLES b) Use your result from a) to…

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Q: 11.Sketch the graph of the region D and evaluate the double integral y dA, D = {(x,y)| 0≤ x ≤ ¹,0 ≤…

A: The region D is bounded by the below curves:x=0 to x=1; y=0 to y=x3.

Q: Find the coordinates of the points of inflection for the function. 14) f(x) = 7e-x²

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Q: Which equation could be represented by the number line? A. -9+8 = -1 B. -4+ (-5) = -9 C. -1 + (-9) =…

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Q: 11. Find the angle between the planes: 4y + 3z = -12 and 3x +2y + 6z = 6.

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Q: Use a system of linear equations with two variables and two equations to solve. 204 students…

A: To find the pass students and fail students.

Q: Use any method to evaluate the integral. dx X>11 (x²-121) 3/2

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Q: d²y dx² - dy - - 6y = 0, when x = 0, y = 0, and when x = 1, y = e³ dx

A: