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Evaluating a Line Integral In Exercises 23-32, evaluate
along each path. (Hint: If F is conservative, the
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Calculus: Early Transcendental Functions
- Using the second fundamental theorem of calculus and chain rule, compute t dt. t+1 dx 2xarrow_forwardдz дz If z = x.f(xy), express x-y in its simplest form.arrow_forwardUse the Fundamental Theorem of Calculus Part I to find dh/dx given h(x) = cost dt (Hint: need substitution here and need to apply the chain rule u as a function of x)arrow_forward
- af af Exercise: Find for f(x. y) = x² + y² ду дх Exercise: Find af ду af дх for f(x. y) = sin xy² x²+1arrow_forwardWrite the function z = xy + x - y in the form F(x, y, z) = 0.arrow_forwardLet f(x) =esin 3x + 2x a. find the linearization of f(x)=esin3x+2x at x=0. b. Use your linearizato to estimate the value of f(0.1).arrow_forward
- Solve using the U-Technique Question 12 Consider f- x(1+yx) dx and using u-substitution in rewriting the integrand as a function of u and du. Determine u if dx is replaced by 2(u – 1)du. (A B 1+Vx x+Vx x+ x/xarrow_forwardWhich is the imaginary part of the analytical complex function f(z)=u(x,y)+i v(x,y) given the real part above?arrow_forwardState and Prove Euler's Theorem on homogeneous functions.arrow_forward
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