Assume that f'' exists and f'' (x) = 0 for all x. Prove that f (x) = mx + b, where m = f'(0) and b = f (0).
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Q: 5. Which of the following functions grow faster than In x as x →o? Which grow at the same rate as In...
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A: As per given data, Since the frame has a width of 2 inches and it covers on two sides, Hence,
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Q: Find the Surface Area rotating around the y-axis
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A: (Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new que...
Q: L’Hôpital’s Rule to evaluate the limit, or state that L’Hôpital’s Rule does not apply.
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Q: Suppose f(1)=2 , f'(-1)=7 , g(1)=2 , g'(1)=3 Find h'(1) for h(x) = f(-x^3)
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Q: 9. If 3f(x) dx = 12, ſ,f(x) dx = 6, and S, g(x) dx = 2, find the values of the following. %3D f(x) d...
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Q: How do we start this question off?
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Q: In Exercises 9–16, express the integrand as a sum of partial fractions and evaluate the integrals. d...
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Q: Could I get the percentage of infection as well and rounded to 2 decimal places?
A: According to product rule of derivative, [f(x)g(x)]’=f’(x)g(x)+f(x)g’(x)
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Q: 32. Water tower Your town has decided to drill a well to increase its water supply. As the town engi...
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Q: How do you answer the question in the attached picture?
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Q: Higher-Order Derivatives f(x)=2x^4-3x^3+2x^2+x+4 find f^4(x) =
A: Let the given function is f(x) = 2x4 -3x3 +2x2 + x + 4. Now we have to find the fourth derivative...
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Q: 82. Use the definitions of the hyperbolic functions to find each of the following limits. b. lim tan...
A: Dear Students, I am solving here 3 parts (a), (b) and (c). In case you need help with the other que...
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Q: In Exercises 25–36, find the derivative of y with respect to the appro- priate variable. 25. y = sin...
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Q: Question 7
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Q: evaluate the limit if it exists. If not, determine whether the one-sided limits exist (finite or inf...
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Q: draw the graph of a function for which f' and f'' take on the given sign combinations. −+, −−, −+
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Q: Solve the initial value problems in Exercises 67–70 for x as a function of t. 67. (² – 3t + 2) = 1 (...
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Q: A round underwater transmission cable consists of a core of copper wires surrounded by nonconducting...
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Q: In Exercises 35–38, solve the initial value problem. dy e¯x-y-2, y(0) = -2 35. dx y Iny 1 + x²' dy 3...
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Q: find a formula for f^(n) if f(x)=x^2e^x
A: We find derivatives of f(x) using product rule.
Q: In Exercises 53 and 54, use a theorem of Pappus to find the centroid of the given triangle. Use the ...
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Q: Find the exact curve x = (y4/8) + (1/4y2), 1 ≤ y ≤ 2
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Q: evaluate the limit.
A: Given:
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A: To determine the implicit derivative of the equation.
Q: Find the area inside one leaf of the polar graph: r = 3cos3x
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Q: find all critical points of f and use the First Derivative Test to determine whether they are local ...
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Q: In this question, the function f is differentiable, and f' (x) = g(x). We don't know exactly what f(...
A: (a) Consider the formula of the chain rule. Use chain rule to compute the derivatives.
Q: 27. The centroid of a triangle lies at the intersection of the trian- gle's medians You may recall t...
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Q: 10. True, or false? As x→0, - (4) b. a. x + 3 = (4) d. 2 + cos x O(2) c. f. xln x = 0(xr²) e. e + x ...
A: Let f(x) and g(x) are the real valued function, both defined on some unbounded subset of the real po...
Q: Give an example of a rational function.
A: Rational function : A fraction which has the property that both its numerator and denominator are po...
Q: compute the derivate
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