5. Compute the derivative of y = (4x + 1)³x. Write an equation of the tangent line to the graph at x= 1.

Q: Use the values in the table below to answer each of the following: x h(x) g(x) h'(x) g'(x) 0 2 1 -5…

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Q: A rectangular field is on Sides and throo side. Find the that area can dimensions by of be enclosed…

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Q: Find the area of the region bounded by the curves y² = x, y - 4 = x, y = -2, and y = 1. (Hint:…

A: Given curve equation:- y2=x,y-4=x,y=-2,y=1

Q: Question Determine the interval of convergence for the power series that can be used to represent…

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Q: ja √√₁²-y² Va2-22 -√a²-y²-√√a²-x² - y² √√a²-x²-y² α ,2 2 ,2 (x²z+y²z+z³) dzdxdy

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Q: 2) Given f(x) = ax²+bx+c has a y-intercept equal to 5, ƒ"(1)= 16, and (1,11) is a point on the…

A: f(x)=ax2+bx+cy intercept is 5f''(1)=16(1,11) is a point on the curve d dx(xn)=nxn-1

Q: For each of the questions below, indicate if the statement is true (T) or false (F). (a) A…

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Q: Suppose f(3) = 4 and f '(3) = 5. Find the indicated values of the derivatives of the following…

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Q: Evaluate the integral. √x² - X 11 dx

A: Here we have to use the concept of integration

Q: ← Let f(x) = 2√x -x. a. Find all points on the graph of f at which the tangent line is horizontal. 1…

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Q: Σ(51)

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Q: Use Newton's Method to approximate the zero(s) of the function. Continue the iterations until two…

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Q: 4 k '(1) = k '(3) = 3 2 1 0 V 0 1 g(x) 2 3 نا 4 X Let k(x) = f(x). Use the graphs above to find the…

A: The graph is given

Q: If f(x)=5x-1, g(0)=2, g'(0)=4, and h(x)=f(g(x)), then what is h'(0)?

A: Solution:

Q: Give the function f(x) = ₁ Evaluate the one-side

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Q: Which of the following is equivalent to 3x²(-2x)e-x² + e-x²16x O -16xe-x²(x² - 1) O 16xe-x²(x² + 1)…

A: Given query is to simplify the expression.

Q: Find the derivate

A: Given ,  g(x)=ln(xex)  We have to find the derivative of g(x) ,  We will find the derivative of g(x)…

Q: Which of the following is not a differential equation? 2 ○ A. t² = s + (d) ² dt OB. y' = 0 C. d² =…

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Q: The area of the region bounded by the curves y = f(x) = 2x³ - 6x² - 2x + 6 and y = g(x) = -x³ + 3x²…

A: First we need to plot the graph

Q: Find the area of the region in the first quadrant (upper right quadrant) bounded by the curves y =…

A: To find the area of the region in the first quadrant (upper right quadrant)  bounded by the curves…

Q: For a sequence {a} satisfying п в U A U C F 4" an A) n=1 ∞ ΣΑ" an B) =1 O Σ6" an n=1 6⁰ an D) n=1…

A: Given that , an+1an→15

Q: Find the absolute maxima for the function: f(x) = 3 Enter the exact answers.

A: We have  fx=3x+sin3xx∈0,2π

Q: 10. (9x² + y - 1) - (4y - x) y' = 0, y(1) = 0

A: We need to find out that the given differential equation is exact or not and if exact then need to…

Q: 2 n² n43 Calculate the following limit. an lim n→∞ bn (Give an exact answer. Use symbolic notation…

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Q: An accessories company finds that the cost and revenue, in dollars, of producing x belts is given by…

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Q: Which of the following series diverge? 2 k² +1 I. IM8 IMS IMS III. k=3 II. Σ k=2 (A) None k 6 (9)*…

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Q: y = sinx, y = csc²x, x Find the area of the region bounded by the curves x = 34. A) 2-√√2 B) 2 +…

A: The given curves are: y=sinx, y=csc2x, x=π4 and x=3π4 Use the common integral formula:…

Q: As a specific example we consider the non-homogeneous problem y" + 25y = sec² (5x) (1) The general…

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Q: A particle is moving in such a way that its displacement xcm from the origin after t seconds is…

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Q: Consider: f(y, y¹) = f (4₁y') = y √ 1+y' ² 2 Upon applying y' yoyyy - f = Cy fe Show that: y = √y ²…

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Q: Which of the following is true? O O O O A B U A) If Σa, converges conditionally, then Σa converges…

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Q: Find u x v, v × u, and v x v. u = 3i + 6k v = 2i + 8j - 3k. (a) UX V -48i + 21j+ 24k eBook (b) VXU…

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Q: n2x–5x2 8x²+2n²

A: We have to find pointwise limit for given function.

Q: Find the critical point of the function: f(x, y) = -1- 6x-2x² - 5y + 3y² (x,y)= This critical point…

A: f(x,y)=-1-6x-2x2-5y+3y2for critical points put ∂f∂x=0∂f∂y=0∂ ∂x(xn)=nxn-1∂ ∂x(constant)=0

Q: f(−3)=10f(−3)=10 and g(−3)=−2g(−3)=−2 Step 1 of 4 :   Find (f+g)(−3)(f+g)(−3).

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Q: Suppose that f is an even function and g is an odd function and both are integrable on the interval…

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Q: Suppose fis continuous on [a, b]. Which of the following is not a definite integral? Jof(x)dx…

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Q: C(x)=2.2x+4,000 and revenues are represented by R(x)=9.4x, which even point?

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Q: Consider the following. x = ln(t), y = 5√t, t≥1 (a) Eliminate the parameter to find a Cartesian…

A: graph

Q: 3. Determine the coordinates of the point(s) on the graph of y = 3x - at which the slope of the…

A: Application of derivative

Q: Let f(x, y) = (x - xy²). In this problem, you will find the absolute maximum and minimum values of…

A: (a) To find critical points, we need to solve for the gradient of f(x, y) and set it equal to zero:…

Q: 2x²+2x+3 Consider the function y= 4x²-4x (a) To use a limit and find its horizontal asymptote what…

A: We have to find out the horizontal asymptote by the use of limits.

Q: If two resistors with resistances R₁ and R₂ are connected in parallel, as shown in the figure, then…

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Q: 8. Find for y=√√4x (arcsin(x²+2x)) dx

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Q: -en y=4x² + 5x, find dy dt when x= -1 and (Simplify your answer.) dx dt = 4,

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Q: Please answer this question asap I will rate you for sure.   Classify the model as Exponential…

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Q: Find the rate of change of total revenue, cost, and profit with respect to time. Assume that R(x)…

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Q: (b) If f(x) has a power series representation about a point x = a with radius of convergence R > 0,…

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Q: Sketch the region of integration and evaluate by changing to polar coordinates: 10 1 1.⁰ [f For…

A: To find:- ∫510∫0fx1x2+y2dydx fx=10x-x2

Q: Use the values in the table below to answer each of the following: x f(x) g(x) f'(x) g'(x) f"(x) 0…

A: The table is given