Find the slope of the graph of the function at the given point. f(x) = √8 - x³, (-2,4) f'(-2) =

Q: Find the first and second derivatives of ƒ(z). Simplify your answer. 7 ƒ(x) = −3x7 P 2

A: Given,

Q: Problem 4: Let f(x)= 42-4 1²-1-6 a. Find the domain of the function. b. Find the y-intercepts, if…

A: The given function is,To find the domain, take the denominator=0So the domain is,

Q: (x) = ₁² ² sin(t) -4x 1+t2 If f(x) = -dt, then f'(x) =

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Q: Let P be the plane containing the point (-11, -2, 1) which is parallel to the plane z + 3y + 4z= -3…

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Q: 1) Let f be the function defined by f(x) = sin(2x) +ecosx . Let g be a differentiable function. The…

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Q: Find the adjoint of the matrix A. Then use the adjoint to find the inverse of A (if possible). (If…

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Q: If we apply Rolle's Theorem to the function f(x) = 2x² - 16x -9 on the interval [2, 6], how many…

A: We will use the concept of Roll's theorem and using this we will solve it.

Q: Find the first, second, and third derivative of the following function. h(x) = (-8x-4)³ a. h'(z) =…

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Q: Find the derivative of the following function using the Fundamental Theorem of Calculus. F'(x) =…

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Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = xy + yz + zx, (1,-1,3),…

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Q: Find the derivative of g u g(x) (2)=√1² +38 du u 5

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Q: The sum of the first 100 terms of the arithmetic series 3 + 1 + (-1) + (-3) + ... is

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Q: Prove the identity. cosh(x) + sinh(x) = ex cosh(x) + sinh(x) = 2²/²/(₁ x + e -x) + ²/² ( 1 = 2/(1 ||

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Q: (a) Use the fact that dtan to find a Taylor series for tan-1 x. dx (b) Using the Taylor series you…

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Q: Using either the triangle inequality or the reverse triangle inequality, prove the following: ii)…

A: To prove the statement |2x−3|≤5 when |x−3|≤1, using the triangle inequality. The triangle inequality…

Q: Let h(x) = 2²-2z - 9 Determine the equation of the tangent line to h at r = 4. Report the solution…

A: We have given a function -9Put 4Point : Differentiating equation with respect to xPut 4Slope(m)=

Q: The view V, or distance in miles, that one can see to the horizon from a height h, in feet, is given…

A: The view V, or distance in miles, that one can see to the horizon from a height h, in feet, is given…

Q: 5. Answer the following questions. (b) (c) Find the direction vector of the line given by parametric…

A: The given  equation of line is

Q: Question 3.13) (see boxed comment above) Is the following function differentiable at x =2? [x² if…

A: The function is differentiable at x=2 if,

Q: 2) Let f be the function given by f(x) = 7xe¹*. a) Find lim f(x) & lim f(x). X118 818 b) Find the…

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Q: Evaluate the following limit by simplifying the expression (first answer box) and then evaluating…

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Q: The sum of the geometric series 7 + 21 + 63 + ... + 413 343 is 826679 620011 413 434 1860 040

A: Formula for geometric series is given as follows nth term of GP is given as follows Sum of n terms…

Q: 2. Consider the function g(x) = 2x³ + 6x² - 18x - 54 a. The y-intercept for the function is: b. The…

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Q: 10. The graph of the function f(x) is shown to the right: Which of the following statements is true…

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Q: Use a graphing utility to graph the quadratic function. f(x) = 2x² + 16x - 32 O -10 -10 -5 f(x) 10 5…

A: Standard form of quadratic equations f(x) = a(x-h) 2 + kWhere vertex: (h, k) Axis of symmetry x=h

Q: Find a linearization at a suitably chosen integer near a at which the given function and its…

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Q: (a) Find the differential dy. y = ex/2 dy = (b) Evaluate dy for the given values of x and dx. x = 0,…

A: The given equation is,Take derivative.

Q: The radius of a sphere is decreasing at a constant rate of 2 meters per minute. At the instant when…

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Q: B 2. Find fæ, fy, fay, fax and fyy for the functions (i) f(x, y) = x²y³ + x³y5; (ii) f(x, y) = x²…

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Q: The position function of a spaceship is r(t) = (6 + t)i + (4 + In(t))j + (9 4 2²² +1 k and the…

A: In the question we have to calculate the time when the engine should be turned off.

Q: 3. Differentiate the following and simplify. a) y = x²-1 x²+1 b) y = sec x tan x

A: (a)

Q: Let f(x) = x+1 Write your answer completely simplified and in factored form. f'(x) =

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Q: 6. ( Determine whether the following two lines are parallel, skew, or intersect. If they intersect,…

A: To determine whether the following lines are parallel, intersecting or skew.If they intersect, then…

Q: For the following exercise, assume that f(x) and g(x) are both differentiable functions of a with…

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Q: Find a general solution to the differential equation using the method of variation of parameters.…

A: The given differential equation is; y''+25y=5csc25t.

Q: The graph of f' (not f) is given below. At which of the marked values of x is A. f(x) greatest x =…

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Q: Solve the given problem and its parts.   What is the implicit equation of the plane through 3D…

A: We will examine two unique subjects pertaining to geometry and computational geometry in this…

Q: 10.Find the area of the triangle with vertices: Q(-1,-3,5), R(-1,-4,7), S(-4,-6,8).

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Q: For the given values of an angle a, find the terminal point P(x, y) on the unit circle. and y= (a)…

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Q: Give a formula for a polynomial function that has x-intercepts at x= -6, x= -5 and x=2 (in typing…

A: A polynomial function has -intercepts at  and .The aim is to find the polynomial function.

Q: The value of parameter k For the differential equation to be exact, it corresponds to…

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Q: Find the derivative the following functions. a) h(x) = 4√√x+3x8 +5ex + π² x³-6x²+8x b) g(x) x²-2x =

A: The given functions are The aim is to find the derivative of the given functions.

Q: 35-36 Find the area enclosed by the given parametric curve and the x-axis. 35. x = ³ + 1, y = 21 -…

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Q: Use spherical coordinates to find the volume of the smaller wedge cut from a sphere of radius 9 by…

A: To findThe volume of the smaller wedge cut from a sphere of radius 9 by two planes that intersect…

Q: Use the Chain Rule to differentiate the following function. 3 f(x)=√x³+√√1-4x4

A: f(x)=x3+1−4x4

Q: If f(x) = 15 1. x f'(x) = 0 t²dt then

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Q: Sketch the graph of a function f with the following properties: f is not continuous when x = 2 but…

A: The given conditionsf is not continuous when  but  exists f has a jump discontinuity when f is…

Q: g(x) = (5+3x)/(x−3) (a) What is the domain of g(x)? (b) Verify (with a sketch and/or short argument)…

A: The given function is

Q: 1. Solve the equation between 0 and 2, 3 sin²(x) + sin(x) = 1 − 3 sin²(x)

A: We are given the trigonometric equation and need to solve it.

Q: If f(x) = √2 + 5x, find f'(5), using the definition of derivative. f'(5) is the limit as x → 5…

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