For the function f(x) given below, find the derivative (-¹)'(c) at the given point c, by first finding a = f-¹(c). If f(x) = 5x + 10x¹7 and c = -15 then a = Using this result, (-¹)'(c) =

Q: If a company spends r million dollars on research, it sales will be s million dollars, where r and s…

A: If a company spends r million dollars on research, it sales will be s million dollars, where r and s…

Q: If f(x)= e^2+In(9) then f" (x)=? Please answer asap and write neatly Thank You.

A: see below the answer and explanation

Q: What is the slope of the line that passes through (1,-1) with y-intercept -2 2 -2 P

A:

Q: The integral in this exercise converges. Evaluate the integral without using a table. 1/5 S x In…

A: To evaluate the given integral

Q: Multiply and simplify: (4x) (8x²) The answer can be written in the form cx where: C= p=

A:

Q: 3. Determine where f(x) = 12x - x³ has any local maximums or any local minimums.

A: To determine maxima or minima for the given function

Q: Use partial fractions to find the indefinite integral. (Remember to use absolute values where…

A:

Q: Find the curvature of the curve r(t) = (4 cos(2t), 4 sin(2t), 2t) at the point t = 0 Give your…

A: The given curve is  r(t)→=4cos(2t), 4sin(2t), 2t

Q: If f(x) + x²[f(x)]4 = 18 and f(1) = 2, find f'(1). f'(1) =

A:

Q: If f(x) + x²[f(x)]4 = 18 and f(1) = 2, find f'(1). f'(1) =

A: As we know that ddx(fg)=f'g+fg'  for two function f and g of x.see below the calculation and answer

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim (ti + cos(t)j +…

A: Given; Limt-pi (ti+cos(t)j+sin(t)k).

Q: Classify the quadric surface. 2² = x² + 1/²/² O hyperboloid of two sheets O elliptic paraboloid O…

A: Given: So,           x2+y29-z2=0 and which is an equation of elliptic paraboloid.

Q: Determine whether the improper integral diverges or converges. 1 e2x + e-2x 1. converges O diverges…

A: Here we have to determine whether the improper integral diverges or converges. I=∫0∞1e2x+e-2xdx

Q: Consider the region bounded by the curve y = 27x − x 4 and the x-axis.  Use Simpson’s Rule with six…

A: Here,             We have given a function now we have to find out the area bounded by the given…

Q: Consider the following cost function. a. Find the average cost and marginal cost functions. b.…

A:

Q: Find aw/as and aw/at using the appropriate Chain Rule. Function Values w = y³ - 5x²y x = es, y = et…

A: Given query is to find indicated partial derivatives.

Q: J ㅌ ation

A: We have to find the value of the given definite using the given information

Q: f(x) = 10 In(x), X [1, e]

A:

Q: Let f(x) 07 O O 11 - S x² + 1 4x – 1 - if x ≤ 1, Determine the value of (ƒ o f)(1). if x > 1.

A: The answer is in step 2.

Q: For each of the following rational functions, determine the horizontal asymptote for the rational…

A:

Q: Use a graphing utility to graph the region bounded by the graphs of the equations. Then find the…

A:

Q: ******** ********* *********** Verify that the function satisfies the three hypotheses of Rolle's…

A:

Q: Find the geometric series or state that it diverges for n=0,infinity        e^-6n

A: We have to write  in geometric series and we have to give state for divergence

Q: Find the indefinite integral. (Note: Solve by the simplest method-not all require integration by…

A: On solving this we will get

Q: Prove the identity. cos (x-y) sinx-sin (x-y) cosx = siny Note that each Statement must be based on a…

A: The objective of the question is proving the identity.

Q: 3-8 Test the series for convergence or divergence. dhe tadt Hour 3.- + - + 1

A: 3. The given series is 47-48+49-410+411-....... We have to find the series is convergence or…

Q: 5 Given sine. and 13 5 0 ₁ + (-1/3) ² - O 5 13 12 13 12 5 ◎[-] 1+ 13 13 12 13 cose= 5 °(9)²+(3)³²-…

A:

Q: A particle moves along the x-axis so that at time t 0 its position is given by x(t) = t³ - 3t² 1.…

A:

Q: Use implicit differentiation to find the points where the parabola defined by x² - 2xy + y² + 4x −…

A:

Q: Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the…

A:

Q: 3.0 Given 2x + 6 3x -6 Find the inverse function f-1, the domain of f-1, and the range of f-¹. f(x)=…

A:

Q: becasue

A:

Q: Given f (x) O-3 O 0 0 1 x+2 =2+2,g(x) = *=², find (ƒ + g) (1)? =

A: See the answer below

Q: rectangular page of a textbook has uniform margins of 2cm on all four sides. If the area of the…

A: Given query is to find the dimensions of the page.

Q: Find '(t), given r(t) r'(t) = = - - 4 -7t 6t? -3t 5' 5t²+1' 4t³ - 3

A:

Q: equation of the line that satisfies the given conditions. Through (4, 7); parallel to the line…

A: Given query is to find the equation of the line.

Q: Consider the initial value problem y" +36y=et, y(0) = yo, y'(0) Suppose we know that y(t) → 0 as…

A: The given differential equation is: y''+36y=e-t Boundary conditions are: y0=y0  ,y'0=y'0yt→0  as t→∞

Q: Suppose 4x² + 16y2 = 100, where x and y are functions of t. dx dy (a) If. = find dt dt 4' dx dt E…

A:

Q: A particle moves along the x-axis so that at time t≥ 0 its velocity is given by v(t) = 3t² − 48t +…

A:

Q: Find the differential dy of the given function. (Use "dx" for dx.) y=x√√√5-x² dy= -2x² + 5 5-r

A: Given function:- y=x5-x2

Q: dz 4-1² Siv Ans. T

A:

Q: Find the following for the given equation. (t)-9²,3a( (a) (e)- (b) (1) (c) Find()).

A: Please see the below picture for detailed solution.

Q: Express the integrand as a sum of partial fractions and evaluate the integral. S 32x² (x-24)(x+8)²…

A:

Q: d. lim x²+5x+6 x²-4 x112 e. limx→∞ (1-x²)³+40x6+x 3x6+3

A: We need to find the limits.

Q: Find the exact length of the curve. = (1 + x²) ³/2, 18 3 20 3 10 3 y 0≤x≤2

A: To find length of the curve.

Q: What is the distance between the point (5,1) and the line with slope 2 and y intercept -2? 13√7 7…

A:

Q: Let r(t) = ( −2+²+2, −3e¹, − 3 sin(2t)). Find fr(t)dt (don't include the +C) fr(t)dt = ([ ])+C

A: Topic = Integration

Q: Find the equation (in terms of xx) of the line through the points (-1,4) and (2,-5) answer is -3x+1

A:

Q: แบบฝึกหัดที่ 1 สูตร m=slope = f'(x₁) - lim m=slope = f'(x) - lim สมการเส้นตรง y = mx+c 15 HO X x-2 3…

A: Disclaimer: “Since you have asked multiple question, we will solve the first question for you. If…

Q: Find the solution to the boundary value problem: d²y dt² dy 2- + 5y = 0, y(0) = 1, y(π, dt

A: