Problem 1. For every real number a, compute the derivative of y = x4 at x = a as a limit of a difference quotient. Show your work.

Q: y(x) = C₁ e ² + C₂ e ²*, + 4 SiN X, Y (0) = 1, y' (0) = -1

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Q: 18. Let P be the curve that follows the helix r = sin / from (1,0,0) to COS / (,), and then returns…

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Q: Differentiate. y = log 4 (x+x) -log 4 (x6 + x) dx =

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Using the appropriate theorems, explain why the function is continuous at every number in its…

A: Given function, f(x)=2x2-x-2x2+4 Function is undefine if x2+4=0x2=-4x2=4i2x=±2i∉R

Q: 9) A rectangle has one corner on the graph of the line y = -x² + 6, another at the origin, a third…

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: 2 = (¹1);^ _'¹1 = (¹) ^ [1 − ₂*x + ²) + × ¹) = (x) ^

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Q: . Find and interpret the derivative at point a. Select the correct answer below and fill in the…

A: Given graph: To find: The derivative at point a =?

Q: = Find the GS of 2xyy' + y² + tan x = = 0

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Q: 1. Graph the following function on the board: f(x)= 0 -∞<x<-1 1+x -1<x<0 1-x 0 0≤x<+1 +1<x<+∞o

A: Please see the below picture for detailed solution.

Q: (a) If f(x) = (x³ − 7x + 11)(x² + 6), compute f'(1). f'(1) (b) If g(x) = = x³ - 7x + 11, compute g…

A: See this solution in below.

Q: Sketch the graph that possesses the characteristics listed. f is concave down at (1,4), concave up…

A: Given,   f concave down = (1,4)   f concave up = (9 , -6)   inflection point = (5 , -1)   graph

Q: Find (f 1)' (a) f(x)=3x³+4x²+6×+5₁ a=5 f(x) = x³ +3 sinx + 2 cosx, q=2 f(x) = 3+x² + ton (₂),…

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Q: A quadratic function f is given. f(x) = 8x² - 16x + 1 (a) Express fin standard form. f(x) =

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Q: the function y = x(x 6)².

A: To find the critical points for the given function

Q: .   Use Simpson's rule with  n = 4  equal subintervals to approximate the following. (Round your…

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Q: If g(s) g'(s) = = 2s²- 19s +6 s² -, compute g'(s). Hint: Simplify g(s) by writing it as a sum of…

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Q: Use the Chain Rule to find dz/dt. z = xy² - x²y, x=t² + 1, y = t²2² - 1

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Q: 2) Suppose that f(3) = 2.5, g (3) = 5, f' (5) = 2.7, f' (3) = 6.2, g (3) = -4, and g' (2.5) = 8. Let…

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Q: Integrate: 16-y4 y³ - dy

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Q: dy Write the function below in the form y=f(u) and u = g(x). Then find as a function of x. dx y = -…

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Q: Determine algebraically whether the function is even, odd, or neither even nor odd f(x) = - 0.72x^2…

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Q: The energy cost of a speed of burst as a function of the body weight of a dolphin is given by…

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Q: Describe the surface. x² + z² = 7 O sphere O ellipsoid O hyperboloid O circular cylinder O elliptic…

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Q: Match the equation with its graph. x² - y² + z² = 1 XX ZA N XK N

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Q: Consider the improper integral [²8 8 + cos(0) 0² Determine if the improper integral converges or…

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Q: main of h(x)= 2 x - - - IS 2122²2 what does f(1) + f(-1) equal? = 2x, what does f(x+1)-f(x - 1)…

A: We have to find the following given condition according to the given information

Q: For the function f(x, y) below, determine whether there is a value for c making the function…

A: The transition value is x = 4   The function f is continuous at all points (x,y) where x is not…

Q: Find a general solution to the differential equation: dx/dt = = x + e^t -- please show all work in…

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Q: Differentiate. f(x) = 8 e 6x f'(x) = [

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Q: Which of these is true? Explain briefly. a. 316 b. 36=2 C. 613

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Q: (a) Find the general solution of dy/dx = 8x³-4x+1. (b) Determine the particular solution such that…

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Q: Consider the function (for question G) S(x) ax³ bx³ + k G. What will happen to lim S(x) if a, b, and…

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Q: Help Entering Answers Find the length of the curve: where 1 < t < 4. Length = M r(t) = 9ti…

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Q: A chemical reaction converts a certain chemical into another chemical, and the rate at which the…

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Q: 9. Let P denote the line segment from (1, −3, 1) to (−5, 3, 8). Compute Sp xy - z dr.

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Q: Question 2 of 12 Your answer is partially correct. f'(x) = lim h→0 20 x3 Equation: y (b) Find the…

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Q: : Find the GS of y' + 2xy + y² = a² −1-x²

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Q: Consider f(x)=5x-3-41/x^2 Find the average rate of change of f(x) with respect to x over the…

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Q: In the above graph of y = f( x ), find the slope of the secant line through the points (-2, f( -2))…

A: We need to find slope of secant line.

Q: On the planet Sulvania, a mountain with an elevation of 1840 feet is the highest peak on the east…

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Q: Find the gradient off and then evaluate the gradient at the point P. a. f(x, y) = x/y, P = (2, 1).…

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Q: 8. f(x,y)=xlnx-yln x

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Q: Solve (a) A x+2y-4 y-2x+3' (6) > c-y-1-

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Q: 1. Find y' of tan(x²y) = 3x + y²

A: Given:      tanx2y4=3x+y2 differentiating on both sides   ddxtanx2y4=ddx3x+y2  Applying…

Q: Write the function below in the form y = f(u) and u = g(x). Then find dx y = -4(sin x)-6 Find dy dx…

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

Q: 86. f(x) = √x, g(x) = 2 x - 4

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Q: 1. A carpenter can construct book cases at a cost of P400 each. If the carpenter sells the book…

A: Given:- Carpenter sells the book cases for x pesos each And 300-2x book cases will be sold per month…

Q: Let A = {1, 6, 9, 7, 5, 10) B=(3, 6, 7, 4} and U be the universal set of natural numbers less than…

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Q: Find a formula for a function g(x,y,z)  whose level surfaces are planes parallel to the plane…

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Q: If f(x)  = 3x2 -x3, find f'(1) and use it to find an equation of the tangent line to the curve  y=…

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